Title: Discrete methods in quantum field theory

Professor Wayne Polyzou; University of Iowa

Abstract: I summarize some results on discrete methods in quantum field theory. I use Daubechies wavelets to construct an exact almost local multi-scale representation of a local quantum field in terms of an infinite collection of well-defined discrete canonical pairs of operators.  This representation has natural volume and resolution truncations.  I show how flow equation methods based on this representation of the Hamiltonian can be used to integrate out short-distance degrees of freedom.  I also discuss a further use of a discrete Weyl representation to approximate irreducible canonical pairs of operators by an irreducible set of discrete operators.  I show how this discrete representation can be used to compute field evolution and scattering observables using a discrete a reinterpretation of real time path integrals as the expectation value of a potential functional with respect to a complex probability distribution on a finite cylinder set of discrete paths.

This is based on work/discussions  with Fatih Bulut, Palle Jorgensen, Brian Kessler, Tracie Michlin, Ekatrina Nathanson and  Jerry Payne