We show in a diagrammatic and regularization independent analysis that the quadratic contribution to the beta function which has been conjectured to render quantum electrodynamics asymptotically free near the Planck scale has its origin in a surface term. Such surface term is intrinsically arbitrarily valued and it is argued to vanish in a consistent treatment of the model.Because of the negative mass dimension of the coupling constant perturbative Einstein quantum gravity (EQG) is nonrenormalizable [1,2]. However one can still make sense of EQG if it is interpreted as an effective quantum field theory within a low energy expansion of a more fundamental theory. In an effective field theory all interactions compatible with its essential symmetry content are in principle allowed into the Lagrangian [3] and thus it establishes a systematic framework to calculate quantum gravitational effects [4].This approach has been used to study the asymptotic behavior at high energies of quantum field theories that incorporate the gravitational field. Robinson and Wilczek suggest that the gravitational field improve the asymptotic freedom of pure Yang-Mills near the Planck scale [5]. However, a similar calculation in the Maxwell-Einstein theory suggests that such conclusion is gauge dependent [6]. In a contribution [7] in which the effective action is calculated in a gauge-condition independent version of the background field method using dimensional regularization it is argued that the gravitational field plays no role in the beta function of the Yang-Mills coupling. Another calculation using conventional diagrammatic methods confirms this conclusion [8].In a recent publication, D. Toms [9] claimed that quadratic divergent contributions were responsible to improve asymptotic freedom of fine structure constant by quantum gravity effects by using * jean@fisica.ufmg.br † lcbrito@dex.ufla.br ‡ msampaio@fisica.ufmg.br § mcnemes@fisica.ufmg.br proper time cutoff regularization and effective action methods. However, the physical reality of the result in [9] has been questioned [10,11]. The purpose of this contribution is to shed light on the origin of such controversies using only a diagrammatic analysis. As an effective model EQG is intrinsically regularization dependent and consequently regularization becomes part of the model. We show however that the quadratic contributions to the beta function stem from ambiguous, arbitrarily valued, regularization dependent surface terms. We present the one loop calculation of the vacuum polarization tensor of the Maxwell-Einstein theory, both with and without matter, in the Feynman and harmonic gauges for the photon and graviton, respectively. We carry out calculations such that regularization ambiguities are isolated from divergent integrals and compare with the results found in the literature showing explicitly the origin of the ambiguities. We evaluate arbitrary parameters in both cutoff and dimensional regularization. Finally we argue that such ambiguities can be fixed on physical grounds d...

The induction of a Lorentz-and CPT-violating Chern-Simons-like term in a fermionic theory embedded in linearized quantum gravity is reassessed. We explicitly show that gauge symmetry on underlying Feynman diagrams does not fix the arbitrariness inherent to such induced term at one loop order. We present the calculation in a nonperturbative expansion in the Lorentz-violating parameter bµ and within a framework which, besides operating in the physical dimension, judiciously parametrizes regularization dependent arbitrary parameters usually fixed by symmetries.

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 calculate explicitly the one-loop effective potential in different Lorentz-breaking field theory models. First, we consider a Yukawa-like theory and some examples of Lorentz-violating extensions of scalar QED. We observe, for the extended QED models, that the resulting effective potential converges to the known result in the limit in which Lorentz symmetry is restored. Besides, the oneloop corrections to the effective potential in all the cases we study depend on the background tensors responsible for the Lorentz-symmetry violation. This has consequences for physical quantities like, for example, in the induced mass due to the Coleman-Weinberg mechanism.