Quantum electrodynamics in the light-front Weyl gauge

Abstract

We examine (3ϩ1)-dimensional QED quantized in the ''front form'' with finite ''volume'' regularization, namely, in discretized light-cone quantization. Instead of the light-cone or Coulomb gauges, we impose the light-front Weyl gauge A Ϫ ϭ0. The Dirac method is used to arrive at the quantum commutation relations for the independent variables. We apply ''quantum-mechanical gauge fixing'' to implement Gauss' law, and derive the physical Hamiltonian in terms of unconstrained variables. As in the instant form, this Hamiltonian is invariant under global residual gauge transformations, namely, displacements. On the light cone the symmetry manifests itself quite differently.

QCD near the light cone

“…See also [12] for a pedagogical review and [13] for a critical discussion focusing on topological aspects. In [14] the method using unitary transformations has been applied to QED quantized on the exact light cone. The above Hamiltonian already is rather complex and nonlocal, just as the most familiar example of a gauge fixed theory, Coulomb gauge QED.…”

Gauge symmetry and the light-front vacuum structure

“…Although the extension of our approach to the vacuum problem of a realistic abelian gauge theory, namely QED(3+1), appeared to be rather straightforward, difficulties related to the renormalization and the presence of non-dynamical zero modes obeying the complicated operator constraints [35] are to be expected. On the other hand, a more general method [29,30,45] of elimination of redundant gauge degrees of freedom by unitary transformations may become a useful alternative to the conventional gauge-fixed formulation of the light-front quantization.…”

Physical and Nonphysical Modes in the Light Front Formulation for the LC Gauge and the Lorentz Gauge Conditions

“…Therefore we may check a simpler possibility by imposing the LC Weyl condition B + = 0. This gauge has been discussed in [11] within the DLCQ quantization and in [12] within the continuous formulation. Here we impose B + = 0 by means of the Lagrange multiplier field Λ into the Lagrangian density (3).…”