We consider an effective model formed by usual QED (minimal coupling) with the addition of a nonminimal Lorentz violating interaction (proportional to a fixed 4-vector bµ) which may radiatively generate both CPT even and odd terms in the pure gauge sector.We show that gauge invariance from usual QED, considered as a limit of the model for bµ → 0, plays an important role in the discussion of the radiatively induced Lorentz violating terms at oneloop order. Moreover, despite the nonrenormalizability of the (effective) model preventing us from readily extending our discussion to higher orders, it is still possible to display the general form of the breaking terms of the photon sector in the on shell limit organized in powers of bµ which in turn can be considered as a small expansion parameter.

We compute the Coulomb correction C to the a. c. conductivity of interacting massless Dirac particles in graphene in the collisionless limit using the polarization tensor approach in a regularization independent framework. Arbitrary parameters stemming from differences between logarithmically divergent integrals are fixed on physical grounds exploiting only spatial O(2) rotational invariance of the model which amounts to transversality of the polarization tensor. Consequently C is unequivocally determined to be (19 − 6π)/12 within this effective model. We compare our result with explicit regularizations and discuss the origin of others results for C found in the literature.

In this paper we consider matter fields in a gravitational background in order to compute the breaking of the conformal current at one-loop order. Standard perturbative calculations of conformal symmetry breaking expressed by the non-zero trace of the energy-momentum tensor have shown that some violating terms are regularization dependent, which may suggest the existence of spurious breaking terms in the anomaly. Therefore, we perform the calculation in a momentum space regularization framework in which regularization dependent terms are judiciously parametrized. We compare our results with those obtained in the literature and conclude that there is an unavoidable arbitrariness in the anomalous term R.

We present a rigorous, regularization independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass µ = 0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy-momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form gµ,νρ with ρ > 0, thus providing a concrete quantum field theoretic model of the Cosmological constant. This ρ represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p ≤ 0. * ggazzola@fisica.ufmg.br † carolina@fisica.ufmg.br ‡ wreszins@fma.if.usp.br 2