276-2 1 Can two or more gauge bosons propagate in the light-front?

Can two or more gauge bosons propagate in the light-front? Gauge fields in the light-front are usually fixed via the n · A = 0 condition yielding the non-local singu-larities of the type (k · n) −α = 0 and α = 1, 2, .. in the gauge boson propagator which must be addressed conveniently. In calculating this propagator for n noncovariant gauge bosons those non-local terms demand the use of a prescription to ensure causality. We show that from 2 gauge bosons onward the implementation of such a prescription does not remove certain pathologies such as the non existence of two or more free propagating gauge bosons in the light-front form. In 1949 Dirac [1], showed that it is possible to construct dynamical forms from the description of a initial state of a given relativistic system in any space-time surface whose lengths between points have no causal connection. The dynamical evolution corresponds to the system following a trajectory throught the hyper-surfaces. For example, the hyper-surface t = 0 is our three-dimensional space. It is invariant under translations and rotations. However, in any transformation of inertial reference frames which involves " boosts " , the temporal coordinate is modified, and therefore the hyper-surface in t = 0. Other hyper-surfaces can be invariant under some type of " boost ". It is the case of the hyperplane called null plane, defined by x + = t + z, which in analogy to the usual coordinate system, is commonly referred to as the " time " coordinate for the front form (light front). For example, a " boost " in the z direction does not modify the null plane. A point in the usual four-dimensional space-time is defined through the set of coordinates x 0 , x 1 , x 2 , x 3 , where x 0 is the time coordinate, that is, x 0 = t, with the usual convention of taking the speed of light equal to unity, c = 1. The other coordinates are the three-dimensional Euclidean space coordinates x 1 = x, x 2 = y and x 3 = z. The light-front coordinates are defined in terms of these by the following relations: