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 and time evolution for the system at instances ; the point form, whose surface is a hyperboloid, and are described by the initial conditions with the constant and and the light front form, whose hypersurface is tangent to the light cone, being defined by the initial conditions at and the “time evolution” for “instances ”. Therefore, the variable 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.
Keywords:
Lorentz Transform; Minkowski Space; Light Front