Lorentz transformations in the light front

Abstract In undergraduate and graduate courses, one usually studies the Lorentz's transformation defined in four-dimensional space: three spatial dimensions and one temporal. In this work we present an alternative way for the Lorentz's transformations using the light front coordinates via Minkowski space-time and its properties. Dirac in one of his works, published in 1949, introduced three different forms of relativistic dynamics: the usual or most common one, called instant form, characterized by the hypersurface specified by the boundary conditions defined at t = 0 and time evolution for the system at instances t > 0; the point form, whose surface is a hyperboloid, and are described by the initial conditions x μ x μ = a 2 with the constant a and t > 0 and the light front form, whose hypersurface is tangent to the light cone, being defined by the initial conditions at x + = c 2 ( t + z c ) = 0 and the “time evolution” for “instances x + > 0”. Therefore, the variable x + plays the role of light-front “time”. The results we present here are connected to the study of Lorentz's transformations using light-cone coordinates and its consequences in the outcome expressions for diverse physical quantities of interest.