T. Heinzl
Theoret.-Physikal. Inst., Universität Jena, Max-Wien-Platz 1
D-07743 Jena, Germany
Abstract:
We review the foundations as well as a number of important applications of light-cone quantization. Beginning with the peculiarities of relativistic particle dynamics we discuss the choice of a time parameter as the gauge fixing within reparametrization invariant dynamical systems. Including Poincaré invariance, we are naturally led to Dirac's forms of relativistic dynamics. Among these, the front form is our main focus as it is the basis for light-cone quantization. We explain the peculiar features of the light-cone formulation such as boost and Galilei invariance or separation of relative and center-of-mass motion. Combining Dirac's front form and field quantization leads to the introduction of light-cone quantum field theory. We show how the positivity of the kinematical longitudinal momentum implies the triviality of the light-cone vacuum. We point out that its special features make the light-cone formulation a unique framework to deal with bound states as few-body systems based on quantum field theory. Our applications will be centered around the issue of spontaneous chiral symmetry breaking and related phenomena. As vacuum properties like e.g. chiral condensates are notoriously elusive in the light-cone formalism, we try to reconstruct those from the particle spectrum. The latter can be obtained by solving the light-cone Schr\"odinger equation as we explicitly demonstrate for the 't~Hooft and Schwinger models. Finally, we make contact with phenomenology by calculating the light-cone wave function of the pion within the Nambu and Jona-Lasinio model. We are thus able to predict a number of observables like the pion charge and core radius, the r.m.s. transverse momentum, the pion form factor and distribution amplitude. The latter turns out to be not very different from the asymptotic one.
The author is grateful for any questions, comments, corrections or criticism, which should be directed to this address t.heinzl@physik.uni-jena.de.