In this paper, we formulate a theory of the second-rank antisymmetric (pseudo)tensor field minimally coupled to a spinor, calculate the one-loop effective potential of the (pseudo)tensor field, and, explicitly, demonstrate that it is positively defined and possesses a continuous set of minima, both for tensor and pseudotensor cases. Therefore, our model turns out to display the dynamical Lorentz symmetry breaking.We also argue that, contrarily to the derivative coupling we use here, derivative-free couplings of the antisymmetric tensor field to a spinor do not generate the positively defined potential and thus do not allow for the dynamical Lorentz symmetry breaking.

We calculate the linearized four-dimensional gravitational Chern-Simons term at the finite temperature, show its finiteness and explicitly demonstrate that its transversal part matches the known result for the chiral vortical conductivity.

In this paper we study the corrections emergent from a Lorentz-violating CPT-odd extension of the complex scalar sector to the Bose-Einstein condensation and to the thermodynamics parameters. We initially discuss some features of the model to only then compute the corrections to the Bose-Einstein condensation. The calculations are done by computing the generating functional, from which we extract the thermodynamics parameters. We also obtain a Lorentz-violating correction for the critical temperature T c that sets the Bose-Einstein condensation.

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In this work, we study the radiative generation of the CPT-odd Lorentz-violating Chern-Simons term, arising from massless fermions. For this, we calculate the vacuum polarization tensor using the 't HooftVeltman regularization scheme, in which the result obtained for the coefficient of the Chern-Simons term is4π 2 b µ . This result leads us precisely to the same conductivity found in Weyl semimetals, i.e., the 't Hooft-Veltman regularization scheme is the correct one to be used in this context. We also discuss the temperature dependence of (k AF ) µ , in which at high temperature, (k AF ) 0 → 0 and (k AF ) i → − e 2 4π 2 b i . In the context of Weyl semimetals, these results are in accordance with the fact that the chiral magnetic current j α = (k AF ) 0 ǫ 0αλρ ∂ λ A ρ vanishes at high temperature, whereas the anomalous Hall current j α = (k AF ) i ǫ iαλρ ∂ λ A ρ remains unaffected by the finite temperature. * Electronic address: jfassuncao,tmariz@fis.ufal.br