Jorge Henrique Sales

Light-front time picture of few-body systems

Abstract 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 Greens functions of the different light-front Fock-states.

Light-front gauge propagator reexamined

Abstract Gauge fields are special in the sense that they are invariant under gauge transformations and “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 · 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 · 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 · A )( ∂ · A ) term in the Lagrangian density. This leads to a well-defined and exact though Lorentz non-invariant propagator.

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·A)2+(∂·A)2 terms in the Lagrangian density. These lead to a well-defined and exact though Lorentz non invariant light-front propagator.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 · A) 2 + (∂ · A) 2 terms in the La-grangian density. These lead to a well-defined and exact though Lorentz non invariant light front propagator.

Zero mode effect generalization for the electromagnetic current in the light front

Instituto de Fisica Teorica UNESP-Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, 01140-070 Sao Paulo, Sao Paulo

Why Pair Production Cures Covariance in the Light-Front?

We show that the light-front vacuum is not trivial, and the Fock space for positive energy quanta solutions is not complete. As an example of this non triviality we have calculated the electromagnetic current for scalar bosons in the background field method were the covariance is restored through considering the complete Fock space of solutions.In this work we construct the electromagnetic current operator for a system composed of two free bosons. The technique employed to deduce these operators is through the definition of global propagators in the light front when a background electromagnetic field acts on one of the particles.

Light Front Boson Model Propagation

The scope and aim of this work is to describe the two-body interaction mediated by a particle (either the scalar or the gauge boson) within the light-front formulation. To do this, first of all we point out the importance of propagators and Green functions in Quantum Mechanics. Then we project the covariant quantum propagator onto the light front time to get the propagator for scalar particles in these coordinates. This operator propagates the wave function from x+ = 0 to x+ > 0. It corresponds to the definition of the time ordering operation in the light front time x+. We calculate the light-front Greens function for 2 interacting bosons propagating forward in x+. We also show how to write down the light front Greens function from the Feynman propagator and finally make a generalization to N bosons.

Light Front Fermion Model Propagation

In this work we consider the propagation of two fermion fields interacting with each other by the exchange of intermediate scalar bosons in the light front. We obtain the corrections up to fourth order in the coupling constant using hierarchical equations in order to obtain the bound state equation (Bethe—Salpeter equation).