arXiv subjects

J. H. O. Sales

Publications and source records attributed to J. H. O. Sales.

27 records · Page 2Linked to original sources

arXiv2004

Quantum gauge boson propagators in the light front

Gauge fields in the light front are traditionally addressed via the employment of an algebraic condition $n\cdot A=0$ in the Lagrangian density, where $A_μ$ is the gauge field (Abelian or non-Abelian) and $n^μ$ is the external, light-like, constant vector which defines the gauge proper. However, this condition though necessary is not sufficient to fix the gauge completely; there still remains a residual gauge freedom that must be addressed appropriately. To do this, we need to define the condition $(n\cdot A)(\partial \cdot A)=0$ with $n\cdot A=0=\partial \cdot A$. The implementation of this condition in the theory gives rise to a gauge boson propagator (in momentum space) leading to conspicuous non-local singularities of the type $(k\cdot n)^{-α}$ where $α=1,2$. These singularities must be conveniently treated, and by convenient we mean not only matemathically well-defined but physically sound and meaningfull as well. In calculating such a propagator for one and two noncovariant gauge bosons those singularities demand from the outset the use of a prescription such as the Mandelstam-Leibbrandt (ML) one. We show that the implementation of the ML prescription does not remove certain pathologies associated with zero modes. However we present a causal, singularity-softening prescription and show how to keep causality from being broken without the zero mode nuisance and letting only the propagation of physical degrees of freedom.

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↗

arXiv2003

Field gauge divergences in the light-front

The Bethe-Salpeter equation for ground state of two fermions exchanging a gauge boson presents divergences. We used a prescription that allowed an apropriate prescription of the singularity in the boson propagator.

nucl-th↗

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↗

arXiv2003

Light-front time picture of few-body systems

The projection of the four-dimensional two-body Bethe-Salpeter equation at the light-front hypersurface is discussed. Elimination of the relative time is performed using a quasi-potential expansion, which is shown to be equivalent to an infinite set of coupled equations for the Green's functions of the different light-front Fock-states.

nucl-th↗

arXiv2003

Light-front time picture of the Bethe-Salpeter equation

We show the light-front representation of the field theoretical Bethe-Salpeter equation (BSE) in the ladder approximation using the quasi potential reduction. We discuss the equivalence of the covariant ladder Bethe-Salpeter equation with an infinite set of coupled equations for the Green's functions of the different light-front Fock-states.

nucl-th↗

arXiv1999

Light-Front Bethe-Salpeter Equation

A three-dimensional reduction of the two-particle Bethe-Salpeter equation is proposed. The proposed reduction is in the framework of light-front dynamics. It yields auxiliary quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded according to the number of particles exchanged at a given light-front time. An example suggests that the convergence of the expansion is rapid. This result is particular for light-front dynamics. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional ones. The technical procedure is developed for a two-boson case; the idea for an extension to fermions is given. The technical procedure appears quite practicable, possibly allowing one to go beyond the ladder approximation for the solution of the Bethe-Salpeter equation. The relation between the three-dimensional light-front reduction of the field-theoretic Bethe-Salpeter equation and a corresponding quantum-mechanical description is discussed.

nucl-th↗

arXiv1998

Pairs in the light-front and covariance

The electromagnetic current of bound systems in the light-front is constructed in the Breit-Frame, in the limit of momentum transfer $q^+=(q^0+q^3)$ vanishing. In this limit, the pair creation term survives and it is responsible for the covariance of the current. The pair creation term is computed for the $j^+$ current of a spin one composite particle in the Breit-frame. The rotational symmetry of $j^+$ is violated if the pair term is not considered.

hep-ph↗