On the group-structure of theories in the infinite momentum frame

Abstract

It is widely believed, that there is a correspondence between infinite momentum frame physics and two-dimensional Galilean physics. This is usually demonstrated by arguing that Weinberg's rule for the old-fashioned perturbation series in the infinite momentum limit can be interpreted as a perturbation series in a two-dimensional Galilean theory. In order to find for this a basis more solid than the usual heuristic arguments, a systematic investigation of the group structure of interacting scalar field theory is performed. It turns out, that the abovementioned correspondence is not necessary. There is a one-parameter freedom in determining the group-structure of the theory in the infinite momentum frame. This parameter has a similar meaning to the velocity of light: when it is finite, one has a relativistic theory, when it is infinite, one has a Galilean theory. It is shown, that Weinberg's above rule may equally well be interpreted as a ‘non-covariant perturbation series’ in a two-dimensional relativistic theory. Possibilities to make use of the two-dimensional relativistic scheme are also discussed.