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.

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

Cosmological model with non-minimally coupled fermionic field

A model for the Universe is proposed whose constituents are: (a) a dark energy field modeled by a fermionic field non-minimally coupled with the gravitational field, (b) a matter field which consists of pressureless baryonic and dark matter fields and (c) a field which represents the radiation and the neutrinos. The coupled system of Dirac's equations and Einstein field equations is solved numerically by considering a spatially flat homogeneous and isotropic Universe. It is shown that the proposed model can reproduce the expected red-shift behaviors of the deceleration parameter, of the density parameters of each constituent and of the luminosity distance. Furthermore, for small values of the red-shift the constant which couples the fermionic and gravitational fields has a remarkable influence on the density and deceleration parameters.Comment: Accepted for publication in Europhysics Letter

Quantum gravitational optics: the induced phase

The geometrical approximation of the extended Maxwell equation in curved spacetime incorporating interactions induced by the vacuum polarization effects is considered. Taking into account these QED interactions and employing the analogy between eikonal equation in geometrical optics and Hamilton-Jacobi equation for the particle motion, we study the phase structure of the modified theory. There is a complicated, local induced phase which is believed to be responsible for the modification of the classical picture of light ray. The main features of QGO could be obtained through the study of this induced phase. We discuss initial principles in conventional and modified geometrical optics and compare the results.Comment: 10 pages, REVTex forma

Spectropolarimetry of the Type IIb Supernova 2001ig

We present spectropolarimetric observations of the Type IIb SN 2001ig in NGC 7424; conducted with the ESO VLT FORS1 on 2001 Dec 16, 2002 Jan 3 and 2002 Aug 16 or 13, 31 and 256 days post-explosion. These observations are at three different stages of the SN evolution: (1) The hydrogen-rich photospheric phase, (2) the Type II to Type Ib transitional phase and (3) the nebular phase. At each of these stages, the observations show remarkably different polarization properties as a function of wavelength. We show that the degree of interstellar polarization is 0.17%. The low intrinsic polarization (~0.2%) at the first epoch is consistent with an almost spherical (<10% deviation from spherical symmetry) hydrogen dominated ejecta. Similar to SN 1987A and to Type IIP SNe, a sharp increase in the degree of the polarization (~1%) is observed when the outer hydrogen layer becomes optically thin by day 31; only at this epoch is the polarization well described by a ``dominant axis.'' The polarization angle of the data shows a rotation through ~40 degrees between the first and second epochs, indicating that the asymmetries of the first epoch were not directly coupled with those observed at the second epoch. For the most polarized lines, we observe wavelength-dependent loop structures in addition to the dominant axis on the Q-U plane. We show that the polarization properties of Type IIb SNe are roughly similar to one another, but with significant differences arising due to line blending effects especially with the high velocities observed for SN 2001ig. This suggests that the geometry of SN 2001ig is related to SN 1993J and that these events may have arisen from a similar binary progenitor system.Comment: 42 pages, 12 figures (figs. 11 and 12 are both composed of four subpanels, figs. 6,7,8,11 and 12 are in color, fig. 1 is low res and a high res version is available at http://www.as.utexas.edu/~jrm/), ApJ Accepte

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

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

A Chiral Schwinger model, its Constraint Structure and Applications to its Quantization

The Jackiw-Rajaraman version of the chiral Schwinger model is studied as a function of the renormalization parameter. The constraints are obtained and they are used to carry out canonical quantization of the model by means of Dirac brackets. By introducing an additional scalar field, it is shown that the model can be made gauge invariant. The gauge invariant model is quantized by establishing a pair of gauge fixing constraints in order that the method of Dirac can be used.Comment: 18 page