743 research outputs found

### Kahler Quantization of H3(CY3,R) and the Holomorphic Anomaly

Studying the quadratic field theory on seven dimensional spacetime
constructed by a direct product of Calabi-Yau three-fold by a real time axis,
with phase space being the third cohomology of the Calabi-Yau three-fold, the
generators of translation along moduli directions of
Calabi-Yau three-fold are constructed. The algebra of these generators is
derived which take a simple form in canonical coordinates. Applying the Dirac
method of quantization of second class constraint systems, we show that the
Schr\"{o}dinger equations corresponding to these generators are equivalent to
the holomorphic anomaly equations if one defines the action functional of the
quadratic field theory with a proper factor one-half.Comment: 10 pages, few typos corrected, to appear in JHE

### New Curved Spacetime Dirac Equations - On the Anomalous Gyromagnetic Ratio

I propose three new curved spacetime versions of the Dirac Equation. These
equations have been developed mainly to try and account in a natural way for
the observed anomalous gyromagnetic ratio of Fermions. The derived equations
suggest that particles including the Electron which is thought to be a point
particle do have a finite spatial size which is the reason for the observed
anomalous gyromagnetic ratio. A serendipitous result of the theory, is that,
two of the equation exhibits an asymmetry in their positive and negative energy
solutions the first suggestion of which is clear that a solution to the problem
as to why the Electron and Muon - despite their acute similarities - exhibit an
asymmetry in their mass is possible. The Mourn is often thought as an Electron
in a higher energy state. Another of the consequences of three equations
emanating from the asymmetric serendipity of the energy solutions of two of
these equations, is that, an explanation as to why Leptons exhibit a three
stage mass hierarchy is possible.Comment: 8 pages, errors corrected, final form of the paper and no further
changes to be made. Accepted in the Foundations of Physics Journa

### A theory of evolving natural constants embracing Einstein's theory of general relativity and Dirac's large number hypothesis

Taking a hint from Dirac's large number hypothesis, we note the existence of
cosmic combined conservation laws that work to cosmologically long time. We
thus modify or generalize Einstein's theory of general relativity with fixed
gravitation constant $G$ to a theory for varying $G$, which can be applied to
cosmology without inconsistency, where a tensor arising from the variation of G
takes the place of the cosmological constant term. We then develop on this
basis a systematic theory of evolving natural constants $m_{e},m_{p},e,\hslash
,k_{B}$ by finding out their cosmic combined counterparts involving factors of
appropriate powers of $G$ that remain truly constant to cosmologically long
time. As $G$ varies so little in recent centuries, so we take these natural
constants to be constant.Comment: 29 pages, revtex

### Unambiguous quantization from the maximum classical correspondence that is self-consistent: the slightly stronger canonical commutation rule Dirac missed

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.Comment: 12 pages, Final publication in Foundations of Physics; available
online at http://www.springerlink.com/content/k827666834140322

### Scale transformation, modified gravity, and Brans-Dicke theory

A model of Einstein-Hilbert action subject to the scale transformation is
studied. By introducing a dilaton field as a means of scale transformation a
new action is obtained whose Einstein field equations are consistent with
traceless matter with non-vanishing modified terms together with dynamical
cosmological and gravitational coupling terms. The obtained modified Einstein
equations are neither those in $f(R)$ metric formalism nor the ones in $f({\cal
R})$ Palatini formalism, whereas the modified source terms are {\it formally}
equivalent to those of $f({\cal R})=\frac{1}{2}{\cal R}^2$ gravity in Palatini
formalism. The correspondence between the present model, the modified gravity
theory, and Brans-Dicke theory with $\omega=-\frac{3}{2}$ is explicitly shown,
provided the dilaton field is condensated to its vacuum state.Comment: 14 pages, accepted for publication in IJT

### Dark energy, antimatter gravity and geometry of the Universe

This article is based on two hypotheses. The first one is the existence of
the gravitational repulsion between particles and antiparticles. Consequently,
virtual particle-antiparticle pairs in the quantum vacuum may be considered as
gravitational dipoles. The second hypothesis is that the Universe has geometry
of a four-dimensional hyper-spherical shell with thickness equal to the Compton
wavelength of a pion, which is a simple generalization of the usual geometry of
a 3-hypersphere. It is striking that these two hypotheses lead to a simple
relation for the gravitational mass density of the vacuum, which is in very
good agreement with the observed dark energy density

### Quantum wave equation of photon

In this paper, we give the quantum wave equations of single photon when it is
in the free or medium space. With these equations, we can study light
interference and diffraction with quantum approach. Otherwise, they can be
applied in quantum optics and photonic crystal.Comment: 8 pages, 0 figure

### A few provoking relations between dark energy, dark matter and pions

I present three relations, striking in their simplicity and fundamental
appearance. The first one connects the Compton wavelength of a pion and the
dark energy density of the Universe; the second one connects Compton wavelength
of a pion and the mass distribution of non-baryonic dark matter in a Galaxy;
the third one relates mass of a pion to fundamental physical constants and
cosmological parameters. All these relations are in excellent numerical
agreement with observations

### Metrical Quantization

Canonical quantization may be approached from several different starting
points. The usual approaches involve promotion of c-numbers to q-numbers, or
path integral constructs, each of which generally succeeds only in Cartesian
coordinates. All quantization schemes that lead to Hilbert space vectors and
Weyl operators---even those that eschew Cartesian coordinates---implicitly
contain a metric on a flat phase space. This feature is demonstrated by
studying the classical and quantum ``aggregations'', namely, the set of all
facts and properties resident in all classical and quantum theories,
respectively. Metrical quantization is an approach that elevates the flat phase
space metric inherent in any canonical quantization to the level of a
postulate. Far from being an unwanted structure, the flat phase space metric
carries essential physical information. It is shown how the metric, when
employed within a continuous-time regularization scheme, gives rise to an
unambiguous quantization procedure that automatically leads to a canonical
coherent state representation. Although attention in this paper is confined to
canonical quantization we note that alternative, nonflat metrics may also be
used, and they generally give rise to qualitatively different, noncanonical
quantization schemes.Comment: 13 pages, LaTeX, no figures, to appear in Born X Proceeding

### Quantum Superposition Principle and Geometry

If one takes seriously the postulate of quantum mechanics in which physical
states are rays in the standard Hilbert space of the theory, one is naturally
lead to a geometric formulation of the theory. Within this formulation of
quantum mechanics, the resulting description is very elegant from the
geometrical viewpoint, since it allows to cast the main postulates of the
theory in terms of two geometric structures, namely a symplectic structure and
a Riemannian metric. However, the usual superposition principle of quantum
mechanics is not naturally incorporated, since the quantum state space is
non-linear. In this note we offer some steps to incorporate the superposition
principle within the geometric description. In this respect, we argue that it
is necessary to make the distinction between a 'projective superposition
principle' and a 'decomposition principle' that extend the standard
superposition principle. We illustrate our proposal with two very well known
examples, namely the spin 1/2 system and the two slit experiment, where the
distinction is clear from the physical perspective. We show that the two
principles have also a different mathematical origin within the geometrical
formulation of the theory.Comment: 10 pages, no figures. References added. V3 discussion expanded and
new results added, 14 pages. Dedicated to Michael P. Ryan on the occasion of
his sixtieth bithda

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