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 $p=5$ or $p=7$. Near the threshold of singularity formation, numerical solutions suggest an approach to self-similarity for the $p=7$ case and an approach to a scale evolving static solution for $p=5$.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