Light-Cone Dynamics of Particles and Fields

We review the foundations as well as a number of important applications of light-cone dynamics. 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 dynamics. 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 light-cone dynamics 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. In a first application, we analyze spontaneous symmetry breaking for scalar field theory in 1+1 dimensions. The importance of modes with vanishing longitudinal momentum is elucidated. For fermionic field theories, we suggest to reconstruct vacuum properties, like chiral condensates, from the particle spectrum. The latter can be obtained by solving the light-cone Schrödinger equation as we explicitly demonstrate for the ’t Hooft and Schwinger models. Finally, we make contact with phenomenology by calculating the pion wave function 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 and the pion distribution amplitude. The latter turns out being not very different from the asymptotic one.