Forms of Relativistic Dynamics

Abstract

Since Dirac wrote his famous article on forms of relativistic dynamics, it has been realized that the front form, or light-front dynamics, is ideally suited for the solution of the bound state problem in quantum field theory. Still, it is useful to know what the other forms are and what makes the front form so well-adapted to non-perturbative problems.

First, a brief discussion is given of the Poincaré group and its connection to different forms of dynamics as described by Dirac. Next the question of equivalence of the different forms of dynamics is discussed. It is shown that the field-theoretical formulae for the Poincaré generators follow Dirac’s classification: kinematic vs. dynamic.

A difficulty that always arises in quantum field theory is the need for regularization to render the results of actual computations finite. In a Hamiltonian framework one cannot immediately apply all methods devised for covariant approaches: e.g. dimensional regularization. Thus new methods must be used and the results compared to calculations carried out in the standard, covariant way. This is done in perturbation theory applied to the case of light-front quantization, where many results are known from the literature, so Hamiltonian methods can be checked explicitly. In this part examples are treated in some detail to illustrate the characteristic features of a light-front calculation.