Renormalization of Lorentz violating theories

We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not generated by renormalization. Renormalizability is ensured by a "weighted power counting" criterion. The theories contain a dimensionful parameter, yet a set of models are classically invariant under a weighted scale transformation, which is anomalous at the quantum level. Formulas for the weighted trace anomaly are derived. The renormalization-group properties are studied.Comment: 28 pages, 1 figure; v2: more references and applications, PRD versio

Renormalizable acausal theories of classical gravity coupled with interacting quantum fields

We prove the renormalizability of various theories of classical gravity coupled with interacting quantum fields. The models contain vertices with dimensionality greater than four, a finite number of matter operators and a finite or reduced number of independent couplings. An interesting class of models is obtained from ordinary power-counting renormalizable theories, letting the couplings depend on the scalar curvature R of spacetime. The divergences are removed without introducing higher-derivative kinetic terms in the gravitational sector. The metric tensor has a non-trivial running, even if it is not quantized. The results are proved applying a certain map that converts classical instabilities, due to higher derivatives, into classical violations of causality, whose effects become observable at sufficiently high energies. We study acausal Einstein-Yang-Mills theory with an R-dependent gauge coupling in detail. We derive all-order formulas for the beta functions of the dimensionality-six gravitational vertices induced by renormalization. Such beta functions are related to the trace-anomaly coefficients of the matter subsector.Comment: 36 pages; v2: CQG proof-corrected versio

On renormalization of power-counting non renormalizable theories

Power-counting non-renormalizable theories should not be dismissed a priori as fundamentaltheories. The practical inconvenient of having infinitely many independentcouplings can be faced in certain cases performing a reduction of couplings. Firstwe study the usage of a special reduction based on the relations imposed by therenormalization group. Then, we analyze the renormalizability of a family of theoriescontaining quantum fields interacting with a classical gravitational field andthat contain a certain class of irrelevant operators. The reduction is this case isguided by a map that also indicates that these models exhibit an acausal behaviorat high energies. Finally, we investigate the renormalizability of models which, althoughcontaining irrelevant operators, are renormalizable with a finite number ofcouplings due to the presence of Lorentz-violating kinetic term. Along this workwe consider models that can violate some principle as the Lorentz symmetry orcausality, but all of them preserve unitarity. The guidelines of this thesis aim toget a better understanding of the role of renormalization as classification tool, andguide the search of a generalization of the Power-Counting criterion that allows theenlargement of the set of candidate fundamental theories

IFUP-TH 2005/22 Dimensionally Continued Infinite Reduction Of Couplings

The infinite reduction of couplings is a tool to consistently renormalize a wide class of non-renormalizable theories with a reduced, eventually finite, set of independent couplings, and classify the non-renormalizable interactions. Several properties of the reduction of couplings, both in renormalizable and non-renormalizable theories, can be better appreciated working at the regularized level, using the dimensional-regularization technique. We show that, when suitable invertibility conditions are fulfilled, the reduction follows uniquely from the requirement that both the bare and renormalized reduction relations be analytic in ε = D − d, where D and d are the physical and continued spacetime dimensions, respectively. In practice, physically independent interactions are distinguished by relatively non-integer powers of ε. We discuss the main physical and mathematical properties of this criterion for the reduction and compare it with other equivalent criteria. The leading-log approximation is solved explicitly and contains sufficient information for the existence and uniqueness of the reduction to all orders. 1