B. L. G. Bakker
Theory Group, Vrije Universiteit Amsterdam, De Boelelaan 1081
NL-1081 HV Amsterdam, The Netherlands
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.
The lectures start with a brief discussion of the Poincare' 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.
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 of the lectures, examples are treated in some detail to illustrate
the characteristic features of a light-front calculation. Finally, the
state of the art in bound-state calculation will be discussed, but not
in any detail. Rather, the connection between the results of perturbative
calculations and the diagonalization of the Hamiltonian will be stressed
here.