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Alfredo T. Suzuki

Publications and source records attributed to Alfredo T. Suzuki.

At least 19 recordsLinked to original sources
arXiv2019

Pauli-Villars Regularization Elucidated in Bopp-Podolsky's Generalized Electrodynamics

We discuss an inherent Pauli-Villars regularization in Bopp-Podolsky's generalized electrodynamics. Introducing gauge-fixing terms for Bopp-Podolsky's generalized electrodynamic action, we realize a unique feature for the corresponding photon propagator with a built-in Pauli-Villars regularization independent of the gauge choice made in Maxwell's usual electromagnetism. According to our realization, the length dimensional parameter $a$ associated with Bopp-Podolsky's higher order derivatives corresponds to the inverse of the Pauli-Villars regularization mass scale $Λ$, i.e. $a = 1/Λ$. Solving explicitly the classical static Bopp-Podolsky's equations of motion for a specific charge distribution, we explore the physical meaning of the parameter $a$ in terms of the size of the charge distribution. As an offspring of the generalized photon propagator analysis, we also discuss our findings regarding on the issue of the two-term vs. three-term photon propagator in light-front dynamics.

hep-th↗
arXiv2004

Surveillance on the light-front gauge fixing Lagrangians

In this work we propose two Lagrange multipliers with distinct coefficients for the light-front gauge that leads to the complete (non-reduced) propagator. This is accomplished via $(n\cdot A)^{2}+(\partial \cdot A)^{2}$ terms in the Lagrangian density. These lead to a well-defined and exact though Lorentz non invariant light front propagator.

hep-th↗
arXiv2004

$ε$-Expansion for non-planar double-boxes

We present calculations for non-planar double-box with four massless/massive external/internal legs/propagators. The results are expressed for arbitrary exponents of propagators and dimension in terms of Lauricella's hypergeometric functions of three variables and hypergeometric-like multiple series.

hep-ph↗
arXiv2003

Light-front gauge propagator reexamined-II

Gauge fields are special in the sense that they are invariant under gauge transformations and \emph{``ipso facto''} they lead to problems when we try quantizing them straightforwardly. To circumvent this problem we need to specify a gauge condition to fix the gauge so that the fields that are connected by gauge invariance are not overcounted in the process of quantization. The usual way we do this in the light-front is through the introduction of a Lagrange multiplier, $(n\cdot A)^{2}$, where $n_μ$ is the external light-like vector, i.e., $n^{2}=0$, and $A_μ$ is the vector potential. This leads to the usual light-front propagator with all the ensuing characteristics such as the prominent $(k\cdot n)^{-1}$ pole which has been the subject of much research. However, it has been for long recognized that this procedure is incomplete in that there remains a residual gauge freedom still to be fixed by some ``ad hoc'' prescription, and this is normally worked out to remedy some unwieldy aspect that emerges along the way. In this work we propose \emph{two} Lagrange multipliers with distinct coefficients for the light-front gauge that leads to the correctly defined propagator with no residual gauge freedom left. This is accomplished via $(n\cdot A)^2+(\partial \cdot A)^2$ terms in the Lagrangian density. These lead to a well-defined and exact though Lorentz non invariant propagator.

hep-th↗
arXiv2003

Light-front gauge propagator reexamined

Gauge fields are special in the sense that they are invariant under gauge transformations and \QTR{em}{``ipso facto''} they lead to problems when we try quantizing them straightforwardly. To circumvent this problem we need to specify a gauge condition to fix the gauge so that the fields that are connected by gauge invariance are not overcounted in the process of quantization. The usual way we do this in the light-front is through the introduction of a Lagrange multiplier, $(n\cdot A)^{2}$, where $n_μ$ is the external light-like vector, i.e., $n^{2}=0$, and $A_μ$ is the vector potential. This leads to the usual light-front propagator with all the ensuing characteristics such as the prominent $(k\cdot n)^{-1}$ pole which has been the subject of much research. However, it has been for long recognized that this procedure is incomplete in that there remains a residual gauge freedom still to be fixed by some ``ad hoc'' prescription, and this is normally worked out to remedy some unwieldy aspect that emerges along the way. In this work we propose a new Lagrange multiplier for the light-front gauge that leads to the correctly defined propagator with no residual gauge freedom left. This is accomplished via $(n\cdot A)(\partial \cdot A)$ term in the Lagrangian density. This leads to a well-defined and exact though Lorentz non invariant propagator.

nucl-th↗
arXiv2002

General Formula for N-point One-loop Feynman Integrals

The negative dimensional integration method (NDIM) is a technique where several difficulties concerning loop integration can be overcome. From usual covariant gauges to complicated Coulomb gauge integrals, and even the trickiest light-cone integrals one can apply the methodology of NDIM. In this work we show how to construct a general formula -- we mean arbitrary exponents of propagators, off-shell external momenta and distinct massive propagators -- for one-loop scalar integrals, for {\it covariant} gauges, and apply it to one through six-point loop integrals. We present detailed analysis of pentagon and hexagon scalar integrals for massive/massless internal particles being external momenta on or off mass shell.

hep-ph↗
arXiv2002

Covariantization and canonical quantization in the light-cone gauge

In the light-cone gauge choice for Abelian and non-Abelian gauge fields, the vector boson propagator carries in it an additional ``spurious'' or ``unphysical'' pole intrinsic to the choice requiring a careful mathematical treatment. Research in this field over the years has shown us that mathematical consistency only is not enough to guarantee physically meaningful results. Whatever the prescription invoked to handle such an object, it has to preserve causality in the process. On the other hand the covariantization technique is a well suited one to tackle gauge dependent poles in the Feynman integrals, dispensing the use of {\em ad hoc} prescriptions. In this work we show that the covariantization technique in the light-cone gauge is a direct consequence of the canonical quantization of the theory.

hep-th↗
arXiv2001

Non-planar double-box, massive and massless pentabox Feynman integrals in negative dimensional approach

Negative dimensional integration method (NDIM) is a technique which can be applied, with success, in usual covariant gauge calculations. We consider three two-loop diagrams: the scalar massless non-planar double-box with six propagators and the scalar pentabox in two cases, where six virtual particles have the same mass and in the case where all of them are massless. Our results are given in terms hypergeometric functions of Mandelstam variables and for arbitrary exponents of propagators and dimension $D$ as well.

hep-th↗
arXiv2001

Obtaining a light-like planar gauge

In the usual and current understanding of planar gauge choices for Abelian and non Abelian gauge fields, the external defining vector $n_μ$ can either be space-like ($n^2<0$) or time-like ($n^2>0$) but not light-like ($n^2=0$). In this work we propose a light-like planar gauge that consists in defining a modified gauge-fixing term, $\cal{L}_{GF}$, whose main characteristic is a two-degree violation of Lorentz covariance arising from the fact that four-dimensional space-time spanned entirely by null vectors as basis necessitates two light-like vectors, namely $n_μ$ and its dual $m_μ$, with $n^2=m^2=0, n\cdot m\neq 0$, say, e.g. normalized to $n\cdot m=2$.

hep-th↗
arXiv2000

Light-cone gauge integrals: Prescriptionlessness at two loops

The only calculations performed beyond one-loop level in the light-cone gauge make use of the Mandelstam-Leibbrandt (ML) prescription in order to circumvent the notorious gauge dependent poles. Recently we have shown that in the context of negative dimensional integration method (NDIM) such prescription can be altogether abandoned, at least in one-loop order calculations. We extend our approach, now studying two-loop integrals pertaining to two-point functions. While previous works on the subject present only divergent parts for the integrals, we show that our prescriptionless method gives the same results for them, besides finite parts for arbitrary exponents of propagators.

hep-th↗
arXiv2000

First results for the Coulomb gauge integrals using NDIM

The Coulomb gauge has at least two advantadges 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 one parameter $ρ$ to regulate the energy integrals. The aim of our work is to apply 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 propagators and dimension.

hep-th↗
arXiv2000

Loop integrals in three outstanding gauges: Feynman, Light-cone and Coulomb

We apply 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, being them originated from any gauge choice. In Feynman gauge we perform scalar two-loop four-point massless integrals; in the light-cone gauge we calculate scalar two-loop integrals contributing for 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; finally, for the Coulomb gauge we consider a four propagator massless loop integral, in the split dimensional regularization context.

hep-th↗
arXiv1999

Solutions for a massless off-shell two-loop three-point vertex

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 simultaneously gives solutions in different regions of external momenta. Moreover, it is a technique whereby the difficulties associated with performing parametric integrals --- the standard approach --- are transferred to a simpler solving of a system of linear algebraic equations. Employing this method, we calculate a massless two-loop three point vertex with all the external legs off-shell. Then NDIM approach allows us to obtain twenty-one distinct new power series representations for the integral in question. In order to verify the correctness of our results, we consider five particular cases where either two of the external legs are put on-shell, or one of them amputated or one exponent of the propagators is set to zero, and compare our results thus obtained with the ones calculated with standard methods in positive dimension.

hep-th↗
arXiv1999

Prescriptionless light-cone integrals

Perturbative quantum gauge field theory seen within the perspective of physical gauge choices such as the light-cone entails the emergence of troublesome poles of the type $(k\cdot n)^{-α}$ in the Feynman integrals, and these come from the boson field propagator, where $α= 1,2,...$ and $n^μ$ is the external arbitrary four-vector that defines the gauge proper. This becomes an additional hurdle to overcome in the computation of Feynman diagrams, since any graph containing internal boson lines will inevitably produce integrands with denominators bearing the characteristic gauge-fixing factor. How one deals with them has been the subject of research for over decades, and several prescriptions have been suggested and tried in the course of time, with failures and successes. However, a more recent development in this front which applies the negative dimensional technique to compute light-cone Feynman integrals shows that we can altogether dispense with prescriptions to perform the calculations. An additional bonus comes attached to this new technique in that not only it renders the light-cone prescriptionless, but by the very nature of it, can also dispense with decomposition formulas or partial fractioning tricks used in the standard approach to separate pole products of the type $(k\cdot n)^{-α}[(k-p)\cdot n]^{-β}$, $(β= 1,2,...)$. In this work we demonstrate how all this can be done.

hep-th↗
arXiv1997

An easy way to solve two-loop vertex integrals

Negative dimensional integration is a step further dimensional regularization ideas. In this approach, based on the principle of analytic continuation, Feynman integrals are polynomial ones and for this reason very simple to handle, contrary to the usual parametric ones. The result of the integral worked out in $D<0$ must be analytically continued again --- of course --- to real physical world, $D>0$, and this step presents no difficulties. We consider four two-loop three-point vertex diagrams with arbitrary exponents of propagators and dimension. These original results give the correct well-known particular cases where the exponents of propagators are equal to unity.

hep-th↗
arXiv1997

Negative Dimensional Integration for Massive Four Point Functions--II: New Solutions

In this sequel calculation of the one-loop Feynman integral pertaining to a massive box diagram contributing to the photon-photon scattering amplitude in quantum electrodynamics, we present the six solutions as yet unknown in the literature. These six new solutions arise quite naturally in the context of negative dimensional integration approach, revealing a promising technique to handle Feynman integrals.

hep-th↗
arXiv1997

Two-loop self-energy diagrams worked out with NDIM

In this work we calculate two two-loop massless Feynman integrals pertaining to self-energy diagrams using NDIM (Negative Dimensional Integration Method). We show that the answer we get is 36-fold degenerate. We then consider special cases of exponents for propagators and the outcoming results compared with known ones obtained via traditional methods.

hep-th↗