The dimensional regularization in light front

We use dimensional regularization (DR) to evaluate a one-loop four-point function to order g2 in a scalar φ4 model using the light-front coordinates and performing the light-front energy variable integration in the first place. The DR in the light-front is applied to the D - 2 transverse variables. We show the equivalence of the result thus obtained with the standard DR applied to D dimensions. © 2013 American Institute of Physics.

A Study of Scattering Amplitude Regularization in the NN System: Two Pions Contributions

In a simplest case we employ dimensional regularization method in order to evaluate the contribution of two pion exchanges to the NN interaction. The method allows one to treat the infinities of scattering amplitude in a way consistent with the symmetries of the theory.

Dimensional versus cut-off renormalization and the nucleon-nucleon interaction

The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.

Probing negative-dimensional integration: Two-loop covariant vertex and one-loop light-cone integrals

The negative-dimensional integration method (NDIM) seems to be a very promising technique for evaluating massless and/or massive Feynman diagrams. It is unique in the sense that the method gives solutions in different regions of external momenta simultaneously. Moreover, it is a technique whereby the difficulties associated with performing parametric integrals in the standard approach are transferred to a simpler solving of a system of linear algebraic equations, thanks to the polynomial character of the relevant integrands. We employ this method to evaluate a scalar integral for a massless two-loop three-point vertex with all the external legs off-shell, and consider several special cases for it, yielding results, even for distinct simpler diagrams. We also consider the possibility of NDIM in non-covariant gauges such as the light-cone gauge and do some illustrative calculations, showing that for one-degree violation of covariance (i.e. one external, gauge-breaking, light-like vector n μ) the ensuing results are concordant with the ones obtained via either the usual dimensional regularization technique, or the use of the principal value prescription for the gauge-dependent pole, while for two-degree violation of covariance - i.e. two external, light-like vectors n μ, the gauge-breaking one, and (its dual) n * μ - the ensuing results are concordant with the ones obtained via causal constraints or the use of the so-called generalized Mandelstam-Leibbrandt prescription. © 1999 Elsevier Science B.V.

Vacuum Polarization Tensor for QED in the Light Front Gauge

The use of light front coordinates in quantum field theories (QFT) always brought some problems and controversies. In this work we explore some aspects of its formalism with respect to the employment of dimensional regularization in the computation of the photon's self-energy at the one-loop level and how the fermion propagator has an important role in the outcoming results.

Do tadpoles vanish in the light-front?

In covariant gauges (CG) regularized with dimensional regularization (DR) it is a standard procedure to set all tadpole Feynman integrals to zero, though; explicitly, they diverge quadratically as the space-time volume. on the other hand, in the notoriously subtle light-front gauge (LTG) some divergent tadpole integrals are said to be nonvanishing, i.e., cannot be set to zero as in the CC case. In this article we analyse the reasons behind this seemingly ambiguous results.

THE GREEN-FUNCTION IN THE BLOCH-NORDSIECK MODEL FOR QED(3)

The electron Green's function is obtained in the Bloch-Nordsieck approximation of three-dimensional QED. Dimensional regularization is used in the intermediate stages of calculation.

Loop Integrals in Three Outstanding Gauges: Feynman, Light-Cone, and Coulomb

We apply the negative dimensional integration method (NDIM) to three outstanding gauges: Feynman, light-cone, and Coulomb gauges. Our aim is to show that NDIM is a very suitable technique to deal with loop integrals, regardless of which gauge choice that originated them. In the Feynman gauge we perform scalar two-loop four-point massless integrals; in the light-cone gauge we calculate scalar two-loop integrals contributing to two-point functions without any kind of prescriptions, since NDIM can abandon such devices - this calculation is the first test of our prescriptionless method beyond one-loop order; and finally, for the Coulomb gauge we consider a four-propagator massless loop integral, in the split-dimensional regularization context. © 2001 Academic Press.

First results for the Coulomb gauge integrals using NDIM

The Coulomb gauge has at least two advantages over other gauge choices in that bound states between quarks and studies of confinement are easier to understand in this gauge. However, perturbative calculations, namely Feynman loop integrations, are not well defined (there are the so-called energy integrals) even within the context of dimensional regularization. Leibbrandt and Williams proposed a possible cure to such a problem by splitting the space-time dimension into D = ω + ρ, i.e., introducing a specific parameter ρ to regulate the energy integrals. The aim of our work is to apply the negative dimensional integration method (NDIM) to the Coulomb gauge integrals using the recipe of split-dimension parameters and present complete results - finite and divergent parts - to the one- and two-loop level for arbitrary exponents of the propagators and dimension.

Gluon mass generation in the PT-BFM scheme

In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. We next present a comprehensive review of several subtle issues relevant to the search of infrared finite solutions, paying particular attention to the role of the seagull graph in enforcing transversality, the necessity of introducing massless poles in the three-gluon vertex, and the incorporation of the correct renormalization group properties. In addition, we present a method for regulating the seagull-type contributions based on dimensional regularization; its applicability depends crucially on the asymptotic behavior of the solutions in the deep ultraviolet, and in particular on the anomalous dimension of the dynamically generated gluon mass. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles belonging to different Lorentz structures. The resulting integral equation is then solved numerically, the infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is determined. Various open questions and possible connections with different approaches in the literature are discussed. © SISSA 2006.

Integração em dimensões negativas em calibres covariantes e não-covariantes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Epstein-Glaser causal approach to the light-front QED(4). II: Vacuum polarization tensor

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A eletrodinâmica escalar generalizada de Duffin-Kemmer-Petiau, uma análise funcional de sua dinâmica quântica covariante e o equilíbrio termodinâmico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Método de integração em dimensão negativa em teoria quântica de campos

This work is a review of the Negative Dimension Integration Method as a powerful tool for the computation of the radiative corrections present in Quantum Field Perturbation Theory. This method is applicable in the context of Dimensional Regularization and it provides exact solutions for Feynman integrals with both dimensional parameter and propagator exponents generalized. These solutions are presentedintheformoflinearcombinationsofhypergeometricfunctionswhosedomains of convergence are related to the analytic structure of the Feynman Integral. Each solution is connected to the others trough analytic continuations. Besides presenting and discussing the general algorithm of the method in a detailed way, we offer concrete applications to scalar one-loop and two-loop integrals as well as to the one-loop renormalizationofQuantumElectrodynamics (QED)