Theory HEP Seminar

An action principle in discrete and continuum space-times

F. Finster

University of Regenburg

We begin by introducing an action principle defined on a finite set of points. This action principle is causal in the sense that it generates a relation on pairs or points which distinguishes between spacelike and timelike separation. In this way, minimizing the action gives rise to a “discrete causal structure”. After generalizing our action principle to include continuum space-times, we review the existence theory and discuss qualitative properties of the minimizers. In the second part of the talk, it is explained how the same action principle can be formulated in Minkowski space to obtain a formulation of quantum field theory. The differences to standard quantum field theory are explained in a simple model where Dirac particles interact via an axial field. We finally outline how to build up more realistic systems which include electroweak and strong forces as well as gravity.