Gauge fields in the light front are traditionally addressed via the employment of an algebraic condition n·A=0 in the Lagrangian density, where Aμ is the gauge field (Abelian or non-Abelian) and nμ 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·A)(∂·A)=0 with n·A=0=∂·A. The implementation of this condition in the theory gives rise to a gauge boson propagator (in momentum space) leading to conspicuous nonlocal singularities of the type (k·n)-α where α=1,2. These singularities must be conveniently treated, and by convenient we mean not only mathemathically well-defined but physically sound and meaningful 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.
Equivalence of light-front and covariant quantum electrodynamics at one-loop level and the form of the gauge boson propagator
