[4] **viXra:0912.0029 [pdf]**
*submitted on 11 Dec 2009*

**Authors:** Z.Y. Wang

**Comments:** 6 pages.

de Broglie formula to photons in an unbounded space is E=hν and λ=h/p. According to
electrodynamics, nevertheless,we prove the ratio E/p in a waveguide is greater than the product νλ
which implies E=hν and p=h/λ cannot be tenable at the same time. Then the Casimir effect is applied
to confirm E=hν and p<h/λ. It is helpful to study quantum tunnelling and superluminality[1]~[2],
Cavity-QED, origin of mass, etc. The microwave experiment to test is also presented.

**Category:** Quantum Physics

[3] **viXra:0912.0006 [pdf]**
*replaced on 8 Aug 2010*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 18 pages, Also archived as arXiv:0910.2490 [physics.gen-ph].

Feynman's Lagrangian path integral was an outgrowth of Dirac's vague surmise that Lagrangians have a
role in quantum mechanics. Lagrangians implicitly incorporate Hamilton's first equation of motion, so their
use contravenes the uncertainty principle, but they are relevant to semiclassical approximations and relatedly
to the ubiquitous case that the Hamiltonian is quadratic in the canonical momenta, which accounts
for the Lagrangian path integral's "success". Feynman also invented the Hamiltonian phase-space path
integral, which is fully compatible with the uncertainty principle. We recast this as an ordinary functional
integral by changing direct integration over subpaths constrained to all have the same two endpoints into
an equivalent integration over those subpaths' unconstrained second derivatives. Function expansion with
generalized Legendre polynomials of time then enables the functional integral to be unambiguously evaluated
through first order in the elapsed time, yielding the Schrödinger equation with a unique quantization
of the classical Hamiltonian. Widespread disbelief in that uniqueness stemmed from the mistaken notion
that no subpath can have its two endpoints arbitrarily far separated when its nonzero elapsed time is made
arbitrarily short. We also obtain the quantum amplitude for any specified configuration or momentum
path, which turns out to be an ordinary functional integral over, respectively, all momentum or all configuration
paths. The first of these results is directly compared with Feynman's mistaken Lagrangian-action
hypothesis for such a configuration path amplitude, with special heed to the case that the Hamiltonian is
quadratic in the canonical momenta.

**Category:** Quantum Physics

[2] **viXra:0912.0005 [pdf]**
*replaced on 15 Mar 2011*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 11 pages, Final publication in Foundations of Physics; available online at
http://www.springerlink.com/content/k827666834140322/

Dirac’s identification of the quantum analog of the Poisson bracket with the commutator is reviewed, as
is the threat of self-inconsistent overdetermination of the quantization of classical dynamical variables which
drove him to restrict the assumption of correspondence between quantum and classical Poisson brackets
to embrace only the Cartesian components of the phase space vector. Dirac’s canonical commutation rule
fails to determine the order of noncommuting factors within quantized classical dynamical variables, but
does imply the quantum/classical correspondence of Poisson brackets between any linear function of phase
space and the sum of an arbitrary function of only configuration space with one of only momentum space.
Since every linear function of phase space is itself such a sum, it is worth checking whether the assumption
of quantum/classical correspondence of Poisson brackets for all such sums is still self-consistent. Not
only is that so, but this slightly stronger canonical commutation rule also unambiguously determines the
order of noncommuting factors within quantized dynamical variables in accord with the 1925 Born-Jordan
quantization surmise, thus replicating the results of the Hamiltonian path integral, a fact first realized by
E. H. Kerner. Born-Jordan quantization validates the generalized Ehrenfest theorem, but has no inverse,
which disallows the disturbing features of the poorly physically motivated invertible Weyl quantization,
i.e., its unique deterministic classical “shadow world” which can manifest negative densities in phase space.

**Category:** Quantum Physics

[1] **viXra:0912.0004 [pdf]**
*submitted on 2 Dec 2009*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 9 pages, Also archived as arXiv:0909.4025 [physics.gen-ph].

It is generally acknowledged that neither the Klein-Gordon equation nor the Dirac Hamiltonian can
produce sound solitary-particle relativistic quantum mechanics due to the ill effects of their negative-energy
solutions; instead their field-quantized wavefunctions are reinterpreted as dealing with particle and
antiparticle simultaneously - despite the clear physical distinguishability of antiparticle from particle and the
empirically known slight breaking of the underlying CP invariance. The natural square-root Hamiltonian
of the free relativistic solitary particle is iterated to obtain the Klein-Gordon equation and linearized to
obtain the Dirac Hamiltonian, steps that have calculational but not physical motivation, and which
generate the above-mentioned problematic negative-energy solutions as extraneous artifacts. Since the natural
square-root Hamiltonian for the free relativistic solitary particle contrariwise produces physically
unexceptionable quantum mechanics, this article focuses on extending that Hamiltonian to describe a solitary
particle (of either spin 0 or spin ½ in relativistic interaction with an external electromagnetic field. That
is achieved by use of Lorentz-covariant solitary-particle four-momentum techniques together with the
assumption that well-known nonrelativistic dynamics applies in the particle's rest frame. Lorentz-invariant
solitary-particle actions, whose formal Hamiltonization is an equivalent alternative approach, are as well
explicitly displayed. It is proposed that two separate solitary-particle wavefunctions, one for a particle
and the other for its antiparticle, be independently quantized in lieu of "reinterpreting" negative-energy
solutions - which indeed don't even afflict proper solitary particles.

**Category:** Quantum Physics