Remarks on Some Results Related to the Thermal Casimir Effect in Einstein and Closed Friedmann Universes with a Cosmic String

In this paper, we present a review of some recent results concerning the thermal corrections to the Casimir energy of massless scalar, electromagnetic, and massless spinor fields in the Einstein and closed Friedmann universes with a cosmic string. In the case of a massless scalar field, it is shown that the Casimir energy can be written as a simple sum of two terms; the first one corresponds to the Casimir energy for the massless scalar field in the Einstein and Friedmann universes without a cosmic string, whereas the second one is simply the Casimir energy of the electromagnetic in this background, multiplied by a parameter λ=(1/α)−1, where α is a constant that codifies the presence of the cosmic string, and is related to its linear mass density, μ, by the expression α=1−Gμ. The Casimir free energy and the internal energy at a temperature different from zero, as well as the Casimir entropy, are given by similar sums. In the cases of the electromagnetic and massless spinor fields, the Casimir energy, free energy, internal energy, and Casimir entropy are also given by the sum of two terms, similarly to the previous cases, but now with both terms related to the same field. Using the results obtained concerning the mentioned thermodynamic quantities, their behavior at high and low temperatures limits are studied. All these results are particularized to the scenario in which the cosmic string is absent. Some discussions concerning the validity of the Nernst heat theorem are included as well.

Projective method for spinorial techniques: Unifying calculational schemes of Dirac amplitudes

There have been numerous approaches to the calculation of spin dependent amplitudes for Dirac particles. All of them have their own advantages, particularly, the standard method of calculation, based on the multiplication by the unit, has a few shortcomings. In this work we use the closure property of the Dirac spinors to present a general method for the amplitude computation. It is shown that the massless spinor method and the helicity spinor method can be formulated through this method. Finally, we get an example of this calculation procedure computing the spin dependentamplitude for the Compton process.

ON THE MYSTERY OF THE MISSING PIE IN GRAPHENE

We investigate the structure of the electromagnetic current density for the pseudorelativistic massless spinor effective model for graphene. It is shown that the pseudorelativistic planar massless Dirac theory in the presence of a constant homogeneous electric field actually leads to the recently measured value for the minimum quantum conductivity.

Fermions as U(1) instantons

Anomalous quantization of the electromagnetic field allows non-trivial (anti) self-dual configurations to exist in four-dimensional Euclidian space-time. These instanton-like objects are described as massless spinor particles.

SOME REMARKS ON THE GRAVITATIONAL AHARONOV–BOHM EFFECT

A massless spinor particle is considered in the background spacetimes generated by a moving mass current and by a spinning cosmic string. In the weak field approximation it is shown that the solution of the Weyl equations depends on the velocity of the source, which does not affect the curvature in this approximation in the case of a moving mass current. In the case of a spinning cosmic string, the solution of the Weyl equations depends on the deficit angle and on the angular momentum of the string. These effects may be viewed as examples of the gravitational analogues of the Aharonov–Bohm effect in electrodynamics.

INCREASE OF THE HAWKING RADIATION FOR SPINOR PARTICLES FROM SCHWARZSCHILD BLACK HOLES BY DIRAC MONOPOLES

An algorithm for numerical computation of the barrier transparency for the potentials surrounding Schwarzschild black holes is described for massless spinor particles. It is then applied to calculate all the configurations (including the contributions of twisted field configurations connected with Dirac monopoles) luminosity for the Hawking radiation from a Schwarzschild black hole. It is found that the contribution due to monopoles can be of order 22% of all the configurations luminosity.

CHIRAL SYMMETRY BREAKING AS A CONSEQUENCE OF NONTRIVIAL SPATIAL TOPOLOGY

A singular configuration of external static magnetic field in the form of a pointlike vortex polarizes the vacuum of quantized massless spinor field in (2+1)-dimensional space–time. This results in an analogue of the Bohm–Aharonov effect: the chiral symmetry breaking condensate, energy density and current emerge in the vacuum even in the case when the spatial region of nonvanishing external field strength is excluded. The dependence of the vacuum characteristics both on the value of the vortex flux and on the choice of the boundary condition at the location of the vortex is determined.