[50] **viXra:0703.0053 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Carl Brannen

**Comments:** recovered from sciprint.org

This paper
eshes out the arguments given in a 20 minute talk at the Phenomenology 2005 meeting
at the University of Wisconsin at Madison, Wisconsin on Monday, May 2, 2005. The argument goes
as follow: A hidden dimension is useful for explaining the phase velocity of quantum waves. The
hidden dimension corresponds to the proper time parameter of standard relativity. This theory has
been developed into a full gravitational theory, "Euclidean Relativity" by other authors. Euclidean
relativity matches the results of Einstein's gravitation theory. This article outlines a compatible
theory for elementary particles.
The massless Dirac equation can be generalized from an equation of matrix operators operating
on vectors to an equation of matrix operators operating on matrices. This allows the Dirac equation
to model four particles simultaneously. We then examine the natural quantum numbers of the
gamma matrices of the Dirac equation, and generalize this result to arbitrary complexified Clifford
algebras. Fitting this "spectral decomposition" to the usual elementary particles, we find that one
hidden dimension is needed as was similarly needed by Euclidean relativity, and that we need a set
of eight subparticles to make up the elementary fermions. These elementary particles will be called
\binons", and each comes in three possible subcolors.
The details of the binding force between binons will be given as a paper associated with a talk
by the author at the APSNW 2005 meeting at the University of Victoria, at British Columbia,
Canada on May 15, 2005. After an abbreviated introduction, this paper will concentrate on the
phenomenological aspects of the binons, particularly as applied to the Centauro type cosmic rays,
and gamma-ray bursts.

**Category:** High Energy Particle Physics

[49] **viXra:0703.0051 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Carlos Castro

**Comments:** recovered from sciprint.org

The large N ...

**Category:** High Energy Particle Physics

[48] **viXra:0703.0050 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Carlos Castro

**Comments:** recovered from sciprint.org

It is shown why the E8 Yang-Mills can be constructed from a Cl(16) algebra Gauge Theory and why
the 11D Chern-Simons (Super) Gravity theory is a very small sector of a more fundamental theory based
on a Cl(11) algebra Gauge theory. These results may shed some light into the origins behind the hidden
E8 symmetry of 11D Supergravity and reveal more important features of a Clifford-algebraic structure
underlying M, F theory.

**Category:** High Energy Particle Physics

[47] **viXra:0703.0049 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Carlos Castro

**Comments:** recovered from sciprint.org

A novel Moyal-Yang star product deformation of generalized p-brane actions in Clifford-space target
backgrounds involving multivectors ( polyvectors, antisymmetric tensors ) valued coordinates is constructed
based on the novel Moyal-Yang star product deformations of Generalized-Yang-Mills theories. ...

**Category:** High Energy Particle Physics

[46] **viXra:0703.0048 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Carlos Castro

**Comments:** recovered from sciprint.org

By recurring to Geometric Probability methods it is shown that the coupling
constants, ...

**Category:** High Energy Particle Physics

[45] **viXra:0703.0047 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Michael Ibison

**Comments:** recovered from sciprint.org

This paper follows in the tradition of direct-action versions of electromagnetism having the aim of
avoiding a balance of infinities wherein a mechanical mass offsets an infinite electromagnetic mass
so as to arrive at a finite observed value. However, the direct-action approach ultimately failed in
that respect because its initial exclusion of self-action was later found to be untenable in the
relativistic domain. Pursing the same end, this paper examines instead a version of
electromagnetism wherein mechanical action is excluded and self-action is retained. It is shown that
the resulting theory is effectively interacting due to the presence of infinite forces. A vehicle for the
investigation is a pair of classical point charges in a positronium-like arrangement for which the
orbits are found to be self-sustaining and naturally quantized.

**Category:** Quantum Physics

[44] **viXra:0703.0046 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Radi I. Khrapko

**Comments:** recovered from sciprint.org

Calculating of absorption of a circularly polarized light beam and an analysis of the celebrated Beth's optics experiment show that the standard electrodynamics needs a concept of classical spin for completing. The spin is presented.

**Category:** Classical Physics

[43] **viXra:0703.0045 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Radi I. Khrapko

**Comments:** recovered from sciprint.org

The impossibility to obtain the electrodynamics Maxwell tensor in the framework of the Lagrange formalism is confirmed by a professor Soper's mistake made on this way. Nevertheless, a heuristic method allows using the Lagrange energy-momentum and spin tensors for obtaining the classical spin tensor.

**Category:** Classical Physics

[42] **viXra:0703.0044 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** R. I. Khrapko

**Comments:** recovered from sciprint.org

According to the standard electrodynamics, a rotating electric dipole emits angular momentum mainly into the equatorial part of space situated near the plane of the rotation where polarization of the radiation is almost linear. Polar regions situated near the axis of rotating are scanty by the angular momentum, although they are intensively illuminated by the almost circularly polarized radiation, which must carries spin angular momentum. A conclusion is made that the electrodynamics sights orbital angular momentum only and overlooks spin. This means that the electrodynamics is not complete. We introduce a spin tensor into the electrodynamics and calculate the whole angular momentum flux radiated by the dipole.

**Category:** Classical Physics

[41] **viXra:0703.0043 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** R. I. Khrapko

**Comments:** recovered from sciprint.org

Roche's paper "What is mass" advocates a historical predecessor of mass. It impedes teaching because presses on inadequate concept of mass.

**Category:** Classical Physics

[40] **viXra:0703.0042 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** R. I. Khrapko

**Comments:** recovered from sciprint.org

A common opinion that a moment of the Poynting vector is spin is a common delusion due to a serious defect of the general field theory. We present a circularly polarized Laguerre-Gaussian beam without an azimuth phase structure as an evidence of this. It is shown that the moment of the Poynting vector in this beam is an orbital angular momentum, not spin. Meanwhile, this beam, as well as a circularly polarized plane wave, clearly carries spin. But the standard electrodynamics does not sight it. Spin tensor of the standard electrodynamics is zero. So, this delusion causes many conflicts, vagueness, and paradoxes concerning electromagnetic angular momentum. The only way to resolve the problems is to use an electrodynamics spin tensor, which we introduced into the electrodynamics and demonstrate in this paper.

**Category:** Classical Physics

[39] **viXra:0703.0041 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** R. I. Khrapko

**Comments:** recovered from sciprint.org

Expressions for a polarized light beam must be corrected to correspond to results of the papers

**Category:** Classical Physics

[38] **viXra:0703.0040 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** R. I. Khrapko

**Comments:** recovered from sciprint.org

It is shown that the quadratic dependence of electric energy on electric strength causes an additional electric energy in comparison with the energy corresponding to a macroscopic electric field. The force acting on a dielectric, in general, does not act on the bound polarization charge. The Maxwell stress tensor in dielectric is considered.

**Category:** Classical Physics

[37] **viXra:0703.0039 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** R. I. Khrapko

**Comments:** recovered from sciprint.org

A celebrated Beth's experiment contradicts the angular momentum conservation law in the frame of Maxwell electrodynamics because Beth's birefringent plate experienced a torque without an angular momentum flux in the surrounding space. However, this paradox can be removed by introducing a classical spin tensor.

**Category:** Classical Physics

[36] **viXra:0703.0038 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Radi I. Khrapko

**Comments:** recovered from sciprint.org

Static electric field in linear uniform neutral dielectric is divergence-free and irrotational. Thus the Maxwell stress tensor is divergence-free as well. So, according to Maxwell, the volume force is ZERO. Only surface forces act on the polarized dielectric.

**Category:** Classical Physics

[35] **viXra:0703.0037 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Radi I. Khrapko

**Comments:** recovered from sciprint.org

Faraday's field lines are not enough for an adequate graphical representation of electromagnetic
fields, It is necessary to use bisurfaces, The bisurfaces and field tubes replacing the field
lines permit to represent evidently for example how electric current creates magnetic field
and electric field produces scalar potential field,
A conception of differential forms and contravariant tensor densities is used, We say that
an exterior derivative of the form or a divergence of the density result in boundaries of the
geometric quantities, The integration of the quantity by the Biot-Savarat formula results in a
new quantity, We name the quantity a generation, Generating from a generation yields zero,
So generations are sterile as well as boundaries are closed. A conjugation is considered The
conjugation converts a closed quantity to a sterile quantity and back, The conjugation differs
from the Hodge operation, The conjugation does not imply a dualization, Chains of field and
an analog of Hodge decomposition theorem are considered

**Category:** Classical Physics

[34] **viXra:0703.0036 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** R. Khrapko

**Comments:** recovered from sciprint.org

We solve the angular momentum problems of the electrodynamics. We show that a desire of using a spin density proved to be correct for evaluating of the electrodynamics spin because the moment of momentum is an orbital angular momentum density and does not encompass the spin. However, the expression is not a true expression for the spin density. This expression yields correct results in simplest cases randomly. Its improvement is hopeless. Instead we present a true spin density of electromagnetic waves and demonstrate a way for its deducing. Our result can be expressed by a sum of the orbital and spin angular momentums.

**Category:** Classical Physics

[33] **viXra:0703.0035 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** R. Khrapko

**Comments:** recovered from sciprint.org

The canonical spin tensor of the standard electrodynamics is inadequate. This is shown by the use of a plane electromagnetic wave and a standing electromagnetic wave as examples. An improvement of the tensor by adding of a magnetic term is considered. The true spin tensor is demonstrated.

**Category:** Classical Physics

[32] **viXra:0703.0034 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Radi I. Khrapko

**Comments:** recovered from sciprint.org

Absorption of a circularly polarized light beam without an azimuth phase structure in a dielectric is calculated in the frame of the standard electrodynamics. We calculate a transfer of energy, momentum, and angular momentum to the dielectric. The calculation shows that the force acting on the dielectric does not have a surface term and the angular momentum flux in the beam equals to two power of the beam divided by frequency. This results contradict an experiment of A. Bishop et al. (PRL, 92, 198104), a paper of R. Loudon (PRA, 68, 013806), and another part of standard electrodynamics, which predicts the flux equals to power of the beam divided by frequency. At the same time the last part of the electrodynamics contradicts to the classical Beth's experiment (PR, 50, 115). To correct this part of the standard electrodynamics we introduce a spin tensor. The corrected electrodynamics is in accordance with our calculation and with the Beth's experiment. But we cannot help the Bishop's and Loudon's results.

**Category:** Classical Physics

[31] **viXra:0703.0033 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** R. I. Khrapko

**Comments:** recovered from sciprint.org

It is shown that the modern Maxwell electrodynamics cannot explain the result of the Beth experiment. So, the modern electrodynamics is not complete. A spin tensor is used for an explanation of the experiment. It is shown that this tensor completes the Maxwell electrodynamics. A theory of the Beth's experiment is presented.

**Category:** Classical Physics

[30] **viXra:0703.0032 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Radi I. Khrapko

**Comments:** recovered from sciprint.org

We calculate absorption of a circularly polarized light beam without an azimuth phase structure in a dielectric in the frame of the standard electrodynamics. A transfer of energy, momentum, and angular momentum from the beam to the dielectric is calculated. The calculation shows, in particular, that the angular momentum flux in the beam equals to two power of the beam divided by frequency. This result contradicts another part of the electrodynamics, which predicts the flux equals to power of the beam divided by frequency. In addition we show that this part of the electrodynamics contradicts the classical Beth's experiment. Our inference is: the electrodynamics is incomplete. To correct the electrodynamics, we introduce a spin tensor into the electrodynamics. The corrected electrodynamics is in accordance with our calculation and with the Beth's experiment.

**Category:** Classical Physics

[29] **viXra:0703.0031 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Chun-Xuan Jiang

**Comments:** recovered from sciprint.org

In this paper using the arithmetic function J2 (w) we prove that there exist infinitely
many integers n such that each of consecutive integers n, n +1,L, n +14 is
exactly k prime factors

**Category:** Number Theory

[28] **viXra:0703.0030 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Chun-Xuan Jiang

**Comments:** recovered from sciprint.org

There cannot be number theory of the twentieth century, the Shimura-Taniyama-Weil conjecture (STWC) and the Langlands program (LP) without the Riemann hypothesis (RH). By using RH it is possible to prove five hundred theorems or more including Wiles' theorem of Fermat's last theorem (FLT) which is false, because RH is disproved.

**Category:** Number Theory

[27] **viXra:0703.0029 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Roger Ellman

**Comments:** recovered from sciprint.org

There can be no non-zero integer solution for n>2 to the equation

**Category:** Number Theory

[26] **viXra:0703.0027 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Radi I. Khrapko

**Comments:** recovered from sciprint.org

Theoretical reasons and results of the works: Phys. Rev. A68 013806 (2003), Opt. Lett. 22 52 (1997), Optics Express 14 6963 (2006), Phys. Rev. Lett. 92 198104 (2004), Phys. Rev. Lett. 91 093602 (2003), Phys. Rev. Lett. 88 053601 (2002) prove that the angular momentum flux carried by a circularly polarized light beam with plane phase front equals two power of the beam divided by the frequency. This fact contradicts the standard electrodynamics, which predicts the beam's angular momentum flux equals power of the beam divided by frequency, and means the electrodynamics is incomplete. To correct the electrodynamics, a spin tensor is used.

**Category:** Classical Physics

[25] **viXra:0703.0026 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Florentin Smarandache

**Comments:** recovered from sciprint.org

Since no fusion theory neither rule fully satisfy all needed applications, the
author proposes a Unification of Fusion Theories and a combination of fusion rules in
solving problems/applications. For each particular application, one selects the most
appropriate model, rule(s), and algorithm of implementation.
We are working in the unification of the fusion theories and rules, which looks like a
cooking recipe, better we'd say like a logical chart for a computer programmer, but we
don't see another method to comprise/unify all things.
The unification scenario presented herein, which is now in an incipient form, should
periodically be updated incorporating new discoveries from the fusion and engineering
research.

**Category:** Artificial Intelligence

[24] **viXra:0703.0025 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** V. Christanto

**Comments:** recovered from sciprint.org

While nowadays it is almost trivial to prove explicitly that
there is exact correspondence (isomorphism) between Dirac equation and
Maxwell electromagnetic equations via biquaternionic representation,
nonetheless their physical meaning remains open for discussion. In the
present note we submit the viewpoint that it would be more conceivable if
we interpret the vierbein in terms of superfluid velocity. Furthermore using
the notion of Hodge bracket operator, we could find a neat linkage between
Dirac equation and Klein-Gordon equation. From this viewpoint it seems
possible to suggest a generalised unified wave equation from relativistic
fluid dynamics, which is thus far never proposed. Furthermore, the present
note argues that it is possible to derive an alternative description of
gravitational phenomena from Aharonov effect in relativistic spacetime,
which then could be used to explain anomalous gravitational phenomenon
known as Podkletnov's experiment. Further experimental observation to
verify or refute this proposition is recommended. For clarity, each new
equation in the present note, which never appears before elsewhere, is
denoted by (#) notation.

**Category:** Quantum Physics

[23] **viXra:0703.0024 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Alex Kaivarainen

**Comments:** recovered from sciprint.org

The original Bivacuum concept developed in this work, like Dirac theory of vacuum, admit
the equal probability of positive and negative energy. The Unified theory (UT) represents
efforts of this author to create the Hierarchical picture of the World, starting from specific
Bivacuum superfluid matrix, providing the elementary particles origination and fields,
excited by particles Corpuscle Wave pulsation.

**Category:** Quantum Physics

[22] **viXra:0703.0023 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** V. Christianto

**Comments:** recovered from sciprint.org

It is known that Barut's equation could predict lepton and
hadron mass with remarkable precision. Recently some authors have
extended this equation, resulting in Barut-Dirac equation. In the present
article we argue that it is possible to derive a new wave equation as
alternative to Barut -Dirac's equation from the known exact correspondence
(isomorphism) between Dirac equation and Maxwell electromagnetic
equations via biquaternionic representation. Furthermore, in the present
note we submit the viewpoint that it would be more conceivable if we
interpret the vierbein of this equation in terms of superfluid velocity, which
in turn brings us to the notion of topological electronic liquid. Some
implications of this proposition include quantization of celestial systems.
We also argue that it is possible to find some signatures of Bose- Einstein
cosmology, which thus far is not explored sufficiently in the literature.
Further experimental observation to verify or refute this proposition is
recommended. For clarity, each new equation in the present note, which
never appears before elsewhere, is denoted by (#) notation.

**Category:** Quantum Physics

[21] **viXra:0703.0021 [pdf]**
*submitted on 18 Mar 2007*

**Authors:** Fu Yuhua

**Comments:** recovered from sciprint.org

Discussing the applications of Dynamic Smarandache Multi-Space (DSMS)
Theory. Supposing for the n different dynamic spaces (n is a dynamic positive integer and
the function of time) the different equations have been established, as these n different
dynamic spaces synthesize the DSMS, and they are mutually affected, some new coupled
equations need to establish in the DSMS to replace some equations in the original dynamic
spaces, as well as supply other equations to process the contact, boundary conditions and
so on. For the unified processing of all equations in the DSMS, this paper proposes to run
the quantization processing to all the variables and all the equations and establish the
unified variational principle of quantization with the collocation method based on the
method of weighted residuals, and simultaneously solve all the equations in the DSMS with
the optimization method. Thus by using the unified variational principle of quantization in
the DSMS and the fractal quantization method, will pave the way for the unified processing
of the theory of relativity and the quantum mechanics, and the unified processing of the
four foundational interactions. Finally the coupled solution for the problem of relativity and
quantum mechanics is discussed.

**Category:** Mathematical Physics

[20] **viXra:0703.0020 [pdf]**
*submitted on 18 Mar 2007*

**Authors:** Mircea Eugen Selariu

**Comments:** recovered from sciprint.org

The discovery of mathematical complements, assembled under the name of the eccentric mathematics, gave the opportunity
for a series of applications, amongst which, in this article, are presented the impulse, step, and unitary ramp functions. The difference,
in comparison with the same classic functions, from the distributions theory, is that those eccentric are periodical with a 2π period. By
combining these between them, new mathematical functions have been defined; united under the name Smarandache stepped
functions.

**Category:** Mathematical Physics

[19] **viXra:0703.0019 [pdf]**
*submitted on 18 Mar 2007*

**Authors:** M. Pitkanen

**Comments:** recovered from sciprint.org

The idea that configuration space CH of 3-surfaces, "the world
of classical worlds", could be realized in terms of number theoretic
anatomies of single space-time point using the real units formed from
infinite rationals, is very attractive.

**Category:** Quantum Physics

[18] **viXra:0703.0018 [pdf]**
*submitted on 18 Mar 2007*

**Authors:** Cao junfeng, Cao Rui

**Comments:** recovered from sciprint.org

In many years study, I've discovered most important force in the nature,
that is cold quantum, under the pressure of cold to hot, the material is
formed, it has the gravity under the cold quantum pressure , then the celestial
body begins to move, cold quantum pressure exists in the space, exists in the
material, it's the cold quantum pressure that makes the formation of four
seasons in the earth, the whirlpool produced from the cold quantum pressure
pushes moving of celestial body, push produces turn and change, cold
freezes the water to ice, there is no other force can do this .People knew the
strong strength of cold quantum, therefore, I said the cold quantum pressure
is the biggest force ever exist in the nature , but there are some people don't
recognize the exist of strong cold quantum, after you have seen this article,
please study it carefully , try to analyze whether I'm right or wrong , if I'm
wrong , please criticize me , if I'm right , please help and support me. Here
I'll express many thanks, at the same time, I'd like to thank all the people
who has helped or supported me.

**Category:** Quantum Gravity and String Theory

[17] **viXra:0703.0017 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** V. Christianto

**Comments:** recovered from sciprint.org

Despite known analogy between condensed matter physics
and various cosmological phenomena, a neat linkage between
low-energy superfluid and celestial quantization is not yet
widely accepted in literature. In the present article we argue
that gravitational Schrödinger equation could be derived from
time-dependent Ginzburg-Landau (or Gross-Pitaevskii) that is
commonly used to describe superfluid dynamics. The solution
for celestial quantization takes the same form with Nottale
equation. Provided this proposed solution corresponds to the
facts, and then it could be used as alternative solution to
predict celestial orbits from quantized superfluid vortice
dynamics. Furthermore, we also discuss a representation of the
wavefunction solution using noncommutative spacetime
coordinate. Some implications of this solution were discussed
particularly in the context of offering a plausible explanation
of the physical origin of quantization of motion of celestial
objects.

**Category:** Quantum Gravity and String Theory

[16] **viXra:0703.0016 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** C. Castro, F. Smarandache

**Comments:** recovered from sciprint.org

This proposal is intended to develop@@ a free digital preprint service for physical sciences to
enable scientists/physicists publishing their preprint articles prior to submitting for formal
publication in scientific journals, or perhaps they only want to see if their idea(s) received
proper response prior to submitting it to journal editors.

**Category:** History and Philosophy of Physics

[15] **viXra:0703.0015 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** Richard Gauthier

**Comments:** recovered from sciprint.org

A spatial model of a free electron (or a positron) is formed by a proposed
superluminally circulating point-like charged superluminal quantum.

**Category:** Quantum Physics

[14] **viXra:0703.0014 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** V. Christianto

**Comments:** recovered from sciprint.org

It is known that the large scale cosmological model may appear resemble to quantum
liquid (Helium).[1] And recently a modified model using this assumption yields a very
good agreement with observed data so far.[2][3] Interestingly, it is also known that
quantum liquid may exhibit quantum computation phenomena, therefore one could say
that a quantum liquid model of universe may appear also as quantum computer. This
aspect, however, has not been explored adequately in literature.

**Category:** Quantum Physics

[13] **viXra:0703.0013 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** Alex Kaivarainen

**Comments:** recovered from sciprint.org

The new quantum Hierarchic theory of condensed matter and theory based computer program
(copyright 1997, USA, Kaivarainen) allow calculating about 300 physical parameters of any
material, including water and ice. Among these parameters are: total internal energy, heat capacity,
thermal conductivity, surface tension, vapor pressure, viscosity, self-diffusion, etc. Most of
intermediate parameters of calculations are hidden for direct experimental measurements

**Category:** Classical Physics

[12] **viXra:0703.0012 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** Carlos Castro

**Comments:** recovered from sciprint.org

We rigorously prove why the proper use ofWeyl's Geometry within the context of
Friedman-Lemaitre-Robertson-Walker cosmological models can account for both the
origins and the value of the observed vacuum energy density ( dark energy )...

**Category:** Relativity and Cosmology

[11] **viXra:0703.0011 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** Gerardo Alvarado

**Comments:** recovered from sciprint.org

I deduce a series which satisfies the fundamental theorem of calculus without dependence on an
explicit function. I prove Taylor's theorem and show that it is closely related. I deduce a series for the
logarithm function and from this series deduce the power series representation of the logarithm function
along with the interval of convergence. I also solve an ordinary differential equation.

**Category:** Functions and Analysis

[10] **viXra:0703.0010 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** Thomas R. Love

**Comments:** recovered from sciprint.org

We construct two first order differential operators which commute
with the operators in a representation of su(2), providing a counterexample
to Schur's Lemma.

**Category:** Quantum Physics

[9] **viXra:0703.0009 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** Diego L. Rapoport

**Comments:** recovered from sciprint.org

We reintroduce the Riemann-Cartan-Weyl geometries with trace
torsion and their associated Brownian motions on spacetime to extend them to
Brownian motions on the tangent bundle and exterior powers of them. We
characterize the diffusion of differential forms, for the case of manifolds without
boundaries and the smooth boundary case. We present implicit representations
for the Navier-Stokes equations (NS) for an incompressible fluid in a smooth
compact manifold without boundary as well as for the kinematic dynamo equation
(KDE, for short) of magnetohydrodynamics. We derive these representations
from stochastic differential geometry, unifying gauge theoretical structures
and the stochastic analysis on manifolds (the Ito-Elworthy formula for differential
forms. From the diffeomorphism property of the random flow given by
the scalar lagrangian representations for the viscous and magnetized fluids, we
derive the representations for NS and KDE, using the generalized Hamilton and
Ricci random flows (for arbitrary compact manifolds without boundary), and
the gradient diffusion processes (for isometric immersions on Euclidean space of
these manifolds). We solve implicitly this equations in 2D and 3D. Continuing
with this method, we prove that NS and KDE in any dimension other than 1,
can be represented as purely (geometrical) noise processes, with diffusion tensor
depending on the fluid's velocity, and we represent the solutions of NS and KDE
in terms of these processes. We discuss the relations between these representations
and the problem of infinite-time existance of solutions of NS and KDE.
We finally discuss the relations between this approach with the low dimensional
chaotic dynamics describing the asymptotic regime of the solutions of NS. We
present the random symplectic theory for the Brownian motions generated by
these Riemann-Cartan-Weyl geometries, and the associated random Poincare-Cartan
invariants. We apply this to the Navier-Stokes and kinematic dynamo
equations. In the case of 2D and 3D, we solve the Hamiltonian equations.

**Category:** Quantum Physics

[8] **viXra:0703.0008 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** Diego L. Rapoport

**Comments:** recovered from sciprint.org

We review the relation between space-time geometries with torsion
fields (the so-called Riemann-Cartan-Weyl (RCW) )geometries) and their
associated Brownian motions. In this setting, the metric conjugate of the tracetorsion
one-form is the drift vectorfield of the Brownian motions. Thus, in
the present approach, Brownian motions, in distinction with Nelson's Stochastic
Mechanics, are spacetime structures. We extend this to the state-space of
non-relativistic quantum mechanics and discuss the relation between a noncanonical
quantum RCW geometry in state-space associated with the gradient
of the quantum-mechanical expectation value of a self-adjoint operator given
by the generalized laplacian operator defined by a RCW geometry. We discuss
the reduction of the wave function in terms of a RCW quantum geometry in
state-space. We characterize the Schroedinger equation for both an observed
and unobserved quantum systems in terms of the RCW geometries and Brownian
motions. Thus, in this work, the Schroedinger field is a torsion generating
field, and the U and R processes, in the sense of Penrose, are associated, the
former to spacetime geometries and their associated Brownian motions, and the
latter to their extension to the state-space of nonrelativistic quantum mechanics
given by the projective Hilbert space. In this setting, the Schroedinger equation
can be either linear or nonlinear. We discuss the problem of the many times
variables and the relation with dissipative processes. We present as an additional
example of RCW geometries and their Brownian motions counterpart, the
dynamics of viscous fluids obeying the invariant Navier-Stokes equations. We
introduce in the present setting an extension of R. Kiehn's approach to dynamical
systems starting from the notion of the topological dimension of one-forms,
to apply it to the trace-torsion one-form whose metric conjugate is the Brownian
motion's drift vectorfield and discuss the topological notion of turbulence. We
discuss the relation between our setting and the Nottale theory of Scale Relativity,
and the work of Castro and Mahecha in this volume in nonlinear quantum
mechanics, Weyl geometries and the quantum potential.

**Category:** Quantum Physics

[7] **viXra:0703.0007 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** Diego L. Rapoport

**Comments:** recovered from sciprint.org

We present the space-time and Hilbert-state space quantum geometries and their associated
Brownian motions. We discuss the problem of the reduction of the wave function associated to
these geometries and their Brownian motions.

**Category:** Quantum Physics

[6] **viXra:0703.0006 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** Carlos Castro

**Comments:** recovered from sciprint.org

By recurring to Geometric Probability methods, it is shown that the coupling constants, ffEM; ffW; ffC
associated with Electromagnetism, Weak and the Strong (color ) force are given by the ratios of the ratios
of the measures of the Shilov boundaries...

**Category:** Classical Physics

[5] **viXra:0703.0005 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** Diego L. Rapoport

**Comments:** recovered from sciprint.org

We present the random representations for the Navier-Stokes
vorticity equations for an incompressible fluid in a smooth manifold with smooth
boundary and reflecting boundary conditions for the vorticity.

**Category:** Classical Physics

[4] **viXra:0703.0004 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** C. Castro, J. A. Nieto, J.F. Gonzalez

**Comments:** recovered from sciprint.org

It is shown how the exact Nonperturbative Renormalization Group flow of the running
Newtonian coupling G(r) in Quantum Einstein Gravity is consistent with the existence
of an ultra-violet cutoff...

**Category:** Relativity and Cosmology

[3] **viXra:0703.0003 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** A.P.Yefremov

**Comments:** recovered from sciprint.org

In the framework of Quaternion (Q-) Theory of Relativity im-plying invariance of the 6D-space-time vector "interval" the kine-matics of two frames is considered under condition that one frame is inertial and the other is subject to action of harmonic force. Us-ing mathematical tools of Q-relativity the cinematic problem is completely solved from the viewpoint of each frame, i.e. distance, velocity and acceleration are found as functions of observers' time. Majority of cinematic relations are revealed to be represented by exact expressions: elementary functions and series; some relations though are found only approximately. Observed motions are of course not harmonic functions. Clock paradox is discussed.

**Category:** Relativity and Cosmology

[2] **viXra:0703.0002 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** Thomas R. Love

**Comments:** recovered from sciprint.org

Lie groups and Lie algebras play a fundamental role in classical mechanics,
electrodynamics, quantum mechanics, relativity, and elementary particle
physics.

**Category:** High Energy Particle Physics

[1] **viXra:0703.0001 [pdf]**
*submitted on 10 Mar 2007*

**Authors:** Carlos Castro

**Comments:** recovered from sciprint.org

A class of proper generalizations of the (Anti) de Sitter solutions are presented
that could provide a very plausible resolution of the cosmological constant problem
along with a natural explanation of the ultraviolet/infrared ( UV/IR) entanglement
required to solve this problem. A nonvanishing value of the vacuum energy density
of the order of 10^-121 M^4_Planck is derived in perfect agreement with the experimental
observations. Exact solutions of the cubic equations associated with the location
of the horizons of this class of ( Anti ) de Sitter-Schwarzschild metrics are found.

**Category:** Relativity and Cosmology