[8] **viXra:1012.0051 [pdf]**
*replaced on 8 Nov 2011*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 12 pages, The physically most appropriate linear mapping into a Schroedinger equation of such an oscillatory classical system that has a symmetric, positive-definite coupling-strength matrix is given in general closed form.
Also archived as arXiv:1101.0168 [physics.gen-ph].

The time-dependent Schrödinger equation with time-independent Hamiltonian matrix is a homogeneous
linear oscillatory system in canonical form. We investigate whether any classical system that itself
is linear, homogeneous, oscillatory and conservative is guaranteed to linearly map into a Schrödinger
equation. Such oscillatory classical systems can be analyzed into their normal modes, which are mutually
independent, uncoupled simple harmonic oscillators, and the equation of motion of such a system linearly
maps into a Schrödinger equation whose Hamiltonian matrix is diagonal, with h times the individual simple
harmonic oscillator frequencies as its diagonal entries. Therefore if the coupling-strength matrix of
such an oscillatory system is presented in symmetric, positive-definite form, the Hamiltonian matrix of the
Schrödinger equation it maps into is h-bar times the square root of that coupling-strength matrix. We obtain
a general expression for mapping this type of oscillatory classical equation of motion into a Schrödinger
equation, and apply it to the real-valued classical Klein-Gordon equation and the source-free Maxwell
equations, which results in relativistic Hamiltonian operators that are strictly compatible with the correspondence
principle. Once such an oscillatory classical system has been mapped into a Schrödinger
equation, it is automatically in canonical form, making second quantization of that Schrödinger equation
a technically simple as well as a physically very interpretable way to quantize the original classical system.

**Category:** High Energy Particle Physics

[7] **viXra:1012.0050 [pdf]**
*submitted on 24 Dec 2010*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 8 pages, Also archived as arXiv:1012.5120 [physics.gen-ph].

It has recently been shown that the classical electric and magnetic fields which satisfy the sourcefree
Maxwell equations can be linearly mapped into the real and imaginary parts of a transverse-vector
wave function which in consequence satisfies the time-dependent Schrödinger equation whose Hamiltonian
operator is physically appropriate to the free photon. The free-particle Klein-Gordon equation for scalar
fields modestly extends the classical wave equation via a mass term. It is physically untenable for complexvalued
wave functions, but has a sound nonnegative conserved-energy functional when it is restricted to
real-valued classical fields. Canonical Hamiltonization and a further canonical transformation maps the
real-valued classical Klein-Gordon field and its canonical conjugate into the real and imaginary parts
of a scalar wave function (within a constant factor) which in consequence satisfies the time-dependent
Schrödinger equation whose Hamiltonian operator has the natural correspondence-principle relativistic
square-root form for a free particle, with a mass that matches the Klein-Gordon field theory's mass term.
Quantization of the real-valued classical Klein-Gordon field is thus second quantization of this natural
correspondence-principle first-quantized relativistic Schrödinger equation. Source-free electromagnetism
is treated in a parallel manner, but with the classical scalar Klein-Gordon field replaced by a transverse
vector potential that satisfies the classical wave equation. This reproduces the previous first-quantized
results that were based on Maxwell's source-free electric and magnetic field equations.

**Category:** High Energy Particle Physics

[6] **viXra:1012.0027 [pdf]**
*submitted on 10 Dec 2010*

**Authors:** Gabriel Di Lemos Santiago Lima

**Comments:** 16 pages

This work is intended to rediscuss the relation between gauge symmetry and current conservation.

**Category:** High Energy Particle Physics

[5] **viXra:1012.0026 [pdf]**
*replaced on 25 Dec 2010*

**Authors:** Gabriel Di Lemos Santiago Lima

**Comments:** 19 pages

This work is intended to estabilish the equivalence between gauge and non-gauge abelian models.
Following a technique proposed by Harada and Tsutsui, it is shown that the Proca and chiral
Schwinger models may be equivalent to correspondent gauge invariant ones. Finally, it is shown
that a gauge invariant version of the chiral Schwinger model, after integrated out the fermions, can
be identified with the 2-D Stueckelberg model without the gauge fixing term.

**Category:** High Energy Particle Physics

[4] **viXra:1012.0025 [pdf]**
*replaced on 27 Dec 2010*

**Authors:** Gabriel Di Lemos Santiago Lima

**Comments:** 16 pages

Reviewing a path-integral procedure of recovering gauge invariance from anomalous effective
actions developed by Harada and Tsutsui in the 80's, it is shown that there is another way to achieve
gauge symmetry, besides the one presented by the authors, which may be anomaly-free, preserving
current conservation. It is also shown that the generalization of Harada-Tsutsui technique to other
models which are not anomalous but do not exhibit gauge invariance allows the identification of
the gauge invariant formulation of the Proca model with the Stueckelberg model, leading to the
interpretation of the gauge invariant mapping as a generalization of the Stueckelberg mechanism.

**Category:** High Energy Particle Physics

[3] **viXra:1012.0023 [pdf]**
*submitted on 9 Dec 2010*

**Authors:** Joseph F. Messina

**Comments:** 2 pages, Published in "Progress in Physics," Vol. 1, 2011.

It is argued that the failure of particle dark matter experiments to verify its existence may be attributable
to a non-Planckian ‘action,’ which renders dark matter’s behavior contradictory to the consequences
of quantum mechanics as it applies to luminous matter. It is pointed out that such a possibility
cannot be convincingly dismissed in the absence of a physical law that prohibits an elementary ‘action’
smaller than Planck’s. It is further noted that no purely dark matter measurement of Planck’s constant
exists. Finally, the possibility of a non-Planckian cold dark matter particle is explored, and found to be
consistent with recent astronomical observations.

**Category:** High Energy Particle Physics

[2] **viXra:1012.0016 [pdf]**
*submitted on 5 Dec 2010*

**Authors:** Alexander G. Kyriakos

**Comments:** 15 pages

In the present paper it is shown that a fully correspondence between the quantum and the electromagnetic
forms of the Dirac electron theory exists, so that each element of the Dirac theory has the known
electrodynamics meaning and vice-versa.

**Category:** High Energy Particle Physics

[1] **viXra:1012.0001 [pdf]**
*submitted on 1 Dec 2010*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 12 pages, Also archived as arXiv:1011.6578 [physics.gen-ph].

Classical equations of motion that are first-order in time and conserve energy can only be quantized
after their variables have been transformed to canonical ones, i.e., variables in which the energy is the
system's Hamiltonian. The source-free version of Maxwell's equations is purely dynamical, first-order in
time and has a well-defined nonnegative conserved field energy, but is decidedly noncanonical. That should
long ago have made source-free Maxwell equation canonical Hamiltonization a research priority, and
afterward, standard textbook fare, but textbooks seem unaware of the issue. The opposite parities of the
electric and magnetic fields and consequent curl operations that typify Maxwell's equations are especially
at odds with their being canonical fields. Transformation of the magnetic field into the transverse part of
the vector potential helps but is not sufficient; further simple nonnegative symmetric integral transforms,
which commute with all differential operators, are needed for both fields; such transforms also supplant
the curls in the equations of motion. The canonical replacements of the source-free electromagnetic fields
remain transverse-vector fields, but are more diffuse than their predecessors, albeit less diffuse than the
transverse vector potential. Combined as the real and imaginary parts of a complex field, the canonical
fields prove to be the transverse-vector wave function of a time-dependent Schrödinger equation whose
Hamiltonian operator is the quantization of the free photon's square-root relativistic energy. Thus proper
quantization of the source-free Maxwell equations is identical to second quantization of free photons that
have normal square-root energy. There is no physical reason why first and second quantization of any
relativistic free particle ought not to proceed in precise parallel, utilizing the square-root Hamiltonian
operator. This natural procedure leaves no role for the completely artificial Klein-Gordon and Dirac
equations, as accords with their grossly unphysical properties.

**Category:** High Energy Particle Physics