Mathematical Physics

1212 Submissions

[7] viXra:1212.0167 [pdf] submitted on 2012-12-31 09:45:17

Nonperturbational "Continued-Fraction" Spin-offs of Quantum Theory's Standard Perturbation Methods

Authors: Steven Kenneth Kauffmann
Comments: 8 Pages.

The inherently homogeneous stationary-state and time-dependent Schroedinger equations are often recast into inhomogeneous form in order to resolve their solution nonuniqueness. The inhomogeneous term can impose an initial condition or, for scattering, the preferred permitted asymptotic behavior. For bound states it provides sufficient focus to exclude all but one of the homogeneous version's solutions. Because of their unique solutions, such inhomogeneous versions of Schroedinger equations have long been the indispensable basis for a solution scheme of successive perturbational corrections which are anchored by their inhomogeneous term. Here it is noted that every such perturbational solution scheme for an inhomogeneous linear vector equation spins off a nonperturbational continued-fraction scheme. Unlike its representation-independent antecedent, the spin-off scheme only works in representations where all components of the equation's inhomogeneous term are nonzero. But that requirement seems to confer theoretical physics robustness heretofore unknown: for quantum fields the order of the perturbation places a bound on unperturbed particle number, the spin-off scheme contrariwise has only basis elements of unbounded unperturbed particle number. It furthermore is difficult to visualize such a continued-fraction spin-off scheme generating infinities, since its successive iterations always go into denominators.
Category: Mathematical Physics

[6] viXra:1212.0164 [pdf] submitted on 2012-12-31 04:19:39

Discrete Structure of Spacetime

Authors: Nicola D'Alfonso
Comments: 4 Pages.

In this paper, I introduce a particular discrete spacetime that should be seriously considered as part of physics because it allows to explain the characteristics of the motion properly, contrary to what happens with the continuous spacetime of the common conception.
Category: Mathematical Physics

[5] viXra:1212.0159 [pdf] submitted on 2012-12-29 08:34:36

The Force of Gravity Belongs to Another Cosmology.

Authors: Dan Visser
Comments: 4 Pages.

This article summarizes theoretical based evidence related to practice for the prediction the universe is not originated from a Big Bang. Instead cosmology could be based on a Double Torus Universe, as is published in my papers in the Vixra-archive. In a few website-articles I also express my vision on the revision of physics and cosmology within this framework. This paper in particular highlights how Gravity could violate General Relativity by a (new) dark energy force in the new Cosmology. This framework contains the connection of the Newton-Gravity force for tiny matter-particles to a dark matter force, producing “+” and “–“ mass-generation, both at scales of about 10^-22 meter. This can cause repulsive gravity in nature. This can open-up a new energy-source for travelling through space by non-relativistic scaling.
Category: Mathematical Physics

[4] viXra:1212.0147 [pdf] submitted on 2012-12-25 15:49:22

Mathematical Theory of Magnetic Field

Authors: Zafar Turakulov
Comments: 9 Pages. no comments

The study of magnetic fields produced by steady currents is a full-valued physical theory which like any other physical theory employs a certain mathematics. This theory has two limiting cases in which source of the field is confined on a surface or a curve. It turns out that mathematical methods to be used in these cases are completely different and differ from from that of the main of the main part of this theory, so, magnetostatics actually consists of three distinct theories. In this work, these three theories are discussed with special attention to the case current carried by a curve. In this case the source serves as a model of thin wire carrying direct current, therefore this theory can be termed magnetostatics of thin wires. The only mathematical method used in this theory till now, is the method of Green's functions. Critical analysis of this method completed in this work, shows that application of this method to the equation for vector potential of a given current density has no foundation and application of this method yields erroneous results
Category: Mathematical Physics

[3] viXra:1212.0128 [pdf] submitted on 2012-12-21 00:50:41

Symmetry-Nondependent Self-Gravitational Upper Bound on Static Local Energy from Use of a Nonperturbative Iteration Method for Lippmann-Schwinger Equations

Authors: Steven Kenneth Kauffmann
Comments: 5 Pages.

It has recently been shown that self-gravitation reduces static spherically-symmetric cumulative energy distributions below the value of their radii times the "Planck force", which is the inverse of G times the fourth power of c. In this article quantitative treatment of self-gravitation is extended to any static energy density that is nonnegative, smooth and globally integrable. The resulting dimensionless local gravitational energy-reduction factor (namely the inverse of the local gravitational time-dilation factor) is shown to satisfy the zero-momentum nonrelativistic Lippmann-Schwinger quantum scattering equation for a repulsive potential which is proportional (with a known coefficient) to that static energy density. Standard perturbative Born-type iteration of Lippmann-Schwinger equations can diverge for sufficiently strong potentials, which in the gravitational case correspond to sufficiently large static energy densities. We have been able, however, to devise an alternate, completely nonperturbative iteration method for Lippmann-Schwinger equations in coordinate representation. Every one of this nonperturbative method's successive approximations to the local gravitational energy-reduction factor turns out to be positive and less than or equal to unity. In consequence, the self-gravitationally corrected static energy contained in any sphere is bounded by that sphere's diameter times the "Planck force".
Category: Mathematical Physics

[2] viXra:1212.0081 [pdf] replaced on 2013-01-06 01:38:58

Unified Integro-Differential Equation for Relaxation and Oscillation

Authors: Hosein Nasrolahpour
Comments: 3 Pages. Another short report on " Fractional Classical Mechanics" :Prespacetime Journal| November 2012 | Volume 3| Issue 13 | pp. 1247-1250

In this paper we discuss some important consequences of application of fractional operators in physics. Also we present a unified integro-differential equation for relaxation and oscillation. We focus on time fractional formalism whose derivative is in Caputo sense.
Category: Mathematical Physics

[1] viXra:1212.0068 [pdf] submitted on 2012-12-10 05:06:49

Mathematical Derivation of the Fine Structure Constant from Fundamental Properties of Natural Numbers

Authors: Otto G. Piringer
Comments: 12 Pages

Recent publications discussed a possible change with time of Sommerfeld's fine structure constant alpha, in which several of the fundamental constants of Nature are combined. The problem of a changing nature of alpha raises the question whether its value is ultimately a result of chance or reveals an objective law of nature. If the value of alpha is independent of human reason, a derivation of it may be possible from basic numbers, like e and pi, which appear in the logical development of mathematics[1]. In the following investigation a pure mathematical derivation of the fine structure constant is described, starting from a fundamental property of natural numbers. The constant alpha results as a limit value in an algorithm with exponential structures.
Category: Mathematical Physics