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

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

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

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

Covariant Hamiltonian Field Theory

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the form of the field equations than the usual Lagrangian description. It is proved that Poisson brackets, Lagrange brackets, and canonical 2-forms exist that are invariant under canonical transformations of the fields. The technique to derive transformation rules for the fields from generating functions is demonstrated by means of various examples. In particular, it is shown that the infinitesimal canonical transformation furnishes the most general form of Noether's theorem. We furthermore specify the generating function of an infinitesimal space-time step that conforms to the field equations.Comment: 93 pages, no figure