3,237 research outputs found
Dirac equation in spacetimes with torsion and non-metricity
Dirac equation is written in a non-Riemannian spacetime with torsion and
non-metricity by lifting the connection from the tangent bundle to the spinor
bundle over spacetime. Foldy-Wouthuysen transformation of the Dirac equation in
a Schwarzschild background spacetime is considered and it is shown that both
the torsion and non-metricity couples to the momentum and spin of a massive,
spinning particle. However, the effects are small to be observationally
significant.Comment: 12 pages LATEX file, no figures, to appear in Int. J. Mod. Phys.
Proca equations derived from first principles
Gersten has shown how Maxwell equations can be derived from first principles,
similar to those which have been used to obtain the Dirac relativistic electron
equation. We show how Proca equations can be also deduced from first
principles, similar to those which have been used to find Dirac and Maxwell
equations. Contrary to Maxwell equations, it is necessary to introduce a
potential in order to transform a second order differential equation, as the
Klein-Gordon equation, into a first order differential equation, like Proca
equations.Comment: 6 page
Threshold of Singularity Formation in the Semilinear Wave Equation
Solutions of the semilinear wave equation are found numerically in three
spatial dimensions with no assumed symmetry using distributed adaptive mesh
refinement. The threshold of singularity formation is studied for the two cases
in which the exponent of the nonlinear term is either or . Near the
threshold of singularity formation, numerical solutions suggest an approach to
self-similarity for the case and an approach to a scale evolving static
solution for .Comment: 6 pages, 7 figure
Gauge invariance and non-constant gauge couplings
It is shown that space-time dependent gauge couplings do not completely break
gauge invariance. We demonstrate this in various gauge theories.Comment: 18 page
Families of stable and metastable solitons in coupled system of scalar fields
In this paper, we obtain stable and metastable soliton solutions of a coupled
system of two real scalar fields with five five discrete points of vacua. These
solutions have definite topological charges and rest energies and show
classical dynamical stability. From a quantum point of view, however, the
V-type solutions are expected to be unstable and decay to D-type solutions. The
induced decay of a V-type soliton into two D-type ones is calculated
numerically, and shown to be chiral, in the sense that the decay products do
not respect left-right symmetry.Comment: 9 pages and 5 figure
Weak-localization and rectification current in non-diffusive quantum wires
We show that electron transport in disordered quantum wires can be described
by a modified Cooperon equation, which coincides in form with the Dirac
equation for the massive fermions in a 1+1 dimensional system. In this new
formalism, we calculate the DC electric current induced by electromagnetic
fields in quasi-one-dimensional rings. This current changes sign, from
diamagnetic to paramagnetic, depending on the amplitude and frequency of the
time-dependent external electromagnetic field.Comment: changed title, added more detail, to appear in J. Phys.: Condens.
Matte
Treating some solid state problems with the Dirac equation
The ambiguity involved in the definition of effective-mass Hamiltonians for
nonrelativistic models is resolved using the Dirac equation. The multistep
approximation is extended for relativistic cases allowing the treatment of
arbitrary potential and effective-mass profiles without ordering problems. On
the other hand, if the Schrodinger equation is supposed to be used, our
relativistic approach demonstrate that both results are coincidents if the
BenDaniel and Duke prescription for the kinetic-energy operator is implemented.
Applications for semiconductor heterostructures are discussed.Comment: 06 pages, 5 figure
Existence of Fermion Zero Modes and Deconfinement of Spinons in Quantum Antiferromagnetism resulting from Algebraic Spin Liquid
We investigate the quantum antiferromagnetism arising from algebraic spin
liquid via spontaneous chiral symmetry breaking. We claim that in the
antiferromagnet massive Dirac spinons can appear to make broad continuum
spectrum at high energies in inelastic neutron scattering. The mechanism of
spinon deconfinement results from the existence of fermion zero modes in single
monopole potentials. Neel vectors can make a skyrmion configuration around a
magnetic monopole of compact U(1) gauge fields. Remarkably, in the
monopole-skyrmion composite potential the Dirac fermion is shown to have a zero
mode. The emergence of the fermion zero mode forbids the condensation of
monopoles, resulting in deconfinement of Dirac spinons in the quantum
antiferromagnet.Comment: K. -S. Kim is much indebted to Dr. A. Tanaka who pointed out a
mistake in association with the gradient expansion in Eq. (C3) and Eq. (C4
Casimir force in the presence of a magnetodielectric medium
In this article we investigate the Casimir effect in the presence of a medium
by quantizing the Electromagnetic (EM) field in the presence of a
magnetodielectric medium by using the path integral formalism. For a given
medium with definite electric and magnetic susceptibilities, explicit
expressions for the Casimir force are obtained which are in agree with the
original Casimir force between two conducting parallel plates immersed in the
quantum electromagnetic vacuum.Comment: 8 pages, 1 figur
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