Special relativity on the light-front

Abstract

P.A.M. Dirac in 1949 showed that it is possible to construct relativistic dynamic forms starting from the description of the initial state of a given relativistic system in any space-time surface whose distances between two points on this hypersurface has no causal connection. The dynamic evolution corresponds to such a system following a trajectory through this hypersurface. For example, the commonest hypersurface of time t = 0 is our three-dimensional (Euclidean) space. It is invariant by rotations and translations. However, in any transformation of inertial frame of references that involves "boosts", the time coordinate is modified and, consequently, the hypersurface at t = 0. Other hypersurfaces may be invariant through some kind of "boost"; the hyperplane that is called null-plane is such a hyperplane, defined by x + = t + z/c, in which c is the speed of light in vacuum, and plays the role of the "time" coordinate in the light-front. The null-plane defined in such a way guarantees that a "boost" in the z direction does not modify the null-plane. Our aim here is to study special relativity under such a transformation of frame of references and see the consequences thereof.