M. C. Nemes

QED with minimal and nonminimal couplings: on the quantum generation of Lorentz-violating terms in the pure photon sector

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 b?) 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 b? ? 0, plays an important role in the discussion of the radiatively induced Lorentz-violating terms at one-loop 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 b? which in turn can be considered as a small expansion parameter.

SYSTEMATIC IMPLEMENTATION OF IMPLICIT REGULARIZATION FOR MULTILOOP FEYNMAN DIAGRAMS

Implicit Regularization (IReg) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. In this work we present a systematic implementation of our method that automatically displays the terms to be subtracted by Bogoliubovs recursion formula. Therefore, we achieve a twofold objective: we show that the IReg program respects unitarity, locality and Lorentz invariance and we show that our method is consistent since we are able to display the divergent content of a multiloop amplitude in a well-defined set of basic divergent integrals in one-loop momentum only which is the essence of IReg. Moreover, we conjecture that momentum routing invariance in the loops, which has been shown to be connected with gauge symmetry, is a fundamental symmetry of any Feynman diagram in a renormalizable quantum field theory.

Arbitrary parameters in implicit regularization and democracy within perturbative description of 2-dimensional gravitational anomalies

We show that the Implicit Regularization Technique is useful to display quantum symmetry breaking in a complete regularization independent fashion. Arbitrary parameters are expressed by finite differences between integrals of the same superficial degree of divergence whose value is fixed on physical grounds (symmetry requirements or phenomenology). We study Weyl fermions on a classical gravitational background in two dimensions and show that, assuming Lorentz symmetry, the Weyl and Einstein Ward identities reduce to a set of algebraic equations for the arbitrary parameters which allows us to study the Ward identities on equal footing. We conclude in a renormalization independent way that the axial part of the Einstein Ward identity is always violated. Moreover whereas we can preserve the pure tensor part of the Einstein Ward identity at the expense of violating the Weyl Ward identities we may as well violate the former and preserve the latter.

Phases of quantum states in completely positive non-unitary evolution

We define an operational notion of phases in interferometry for a quantum system undergoing a completely positive non-unitary evolution. This definition is based on the concepts of quantum measurement theory. The suitable generalization of the Pancharatnan connection allows us to determine the dynamical and geometrical parts of the total phase between two states linked by a completely positive map. These results reduce to the known expressions of the total, dynamical and geometrical phases for pure and mixed states evolving unitarily.

Implicit regularization beyond one-loop order: gauge field theories

We extend a constrained version of implicit regularization (CIR) beyond one-loop order for gauge field theories. In this framework, the ultraviolet content of the model is displayed in terms of momentum loop integrals order by order in perturbation theory for any Feynman diagram, while the Ward–Slavnov–Taylor identities are controlled by finite surface terms. To illustrate, we apply CIR to massless abelian gauge field theories (scalar and spinorial QED) to two-loop order and calculate the two-loop beta-function of spinorial QED.

Experimental proposal for measuring the Gouy phase of matter waves

The Schr?dinger equation for an atomic beam predicts that it must have a phase anomaly near the beam waist analogous to the Gouy phase of an electromagnetic beam. We propose here a feasible experiment that allows for direct determination of this anomalous phase using Ramsey interferometry with Rydberg atoms. Possible experimental limitations are discussed, and shown to be completely under control within present-day technology. We also discuss how this finding can open the possibility of using the spatial mode wavefunctions of atoms as q-dits, since the Gouy phase is an essential ingredient for making rotations in the quantum states.

(Un)determined finite regularization dependent quantum corrections: the Higgs boson decay into two photons and the two photon scattering examples

We investigate the appearance of arbitrary, regularization dependent parameters introduced by divergent integrals in two a priori finite but superficially divergent amplitudes: the Higgs decay into two photons and the two photon scattering. We use a general parametrization of ultraviolet divergences which makes explicit such ambiguities. Thus we separate in a consistent way using Implicit Regularization the divergent, finite and regularization dependent parts of the amplitudes which in turn are written as surface terms. We find that, although finite, these amplitudes are ambiguous before the imposition of physical conditions namely momentum routing invariance in the loops of Feynman diagrams. In the examples we study momentum routing invariance turns out to be equivalent to gauge invariance. We also discuss the results obtained by different regularizations and show how they can be reproduced within our framework allowing for a clear view on the origin of regularization ambiguities.

Implicit regularization beyond one-loop order: scalar field theories

Implicit regularization (IR) has been shown as a useful momentum space tool for perturbative calculations in dimension-specific theories, such as chiral gauge, topological and supersymmetric quantum field theoretical models at one-loop level. In this paper, we aim at generalizing systematically IR to be applicable beyond one-loop order. We use a scalar field theory as an example and pave the way for the extension to quantum field theories which are richer from the symmetry content viewpoint. Particularly, we show that a natural (minimal) renormalization scheme emerges, in which the infinities displayed in terms of integrals in one internal momentum are subtracted, whereas infrared and ultraviolet modes do not mix and therefore leave no room for ambiguities. A systematic cancellation of the infrared divergences at any loop order takes place between the ultraviolet finite and divergent parts of the amplitude for non-exceptional momenta leaving, as a by-product, a renormalization group scale.

Supergravity corrections to the (g−2)l factor by implicit regularization

We apply implicit regularization in the calculation of the one-loop graviton and gravitino corrections to the anomalous magnetic moment of the lepton in unbroken supergravity. This is an important test for any regularization method. We find a null result as it is expected from supersymmetry. We compare our results with the ones obtained by using differential regularization and dimensional reduction, which are known to preserve supersymmetry at one-loop order.

On the equivalence between implicit regularization and constrained differential renormalization

Constrained differential renormalization (CDR) and the constrained version of implicit regularization are two regularization independent techniques that do not rely on dimensional continuation of the space-time. These two methods, which have rather distinct bases, have been successfully applied to several calculations, which show that they can be trusted as practical, symmetry invariant frameworks (gauge and supersymmetry included) in perturbative computations even beyond one-loop order. In this paper, we show the equivalence between these two methods at one-loop order. We show that the configuration space rules of CDR can be mapped into the momentum-space procedures of implicit regularization, the major principle behind this equivalence being the extension of the properties of regular distributions to regularized ones.