Boost invariant regulator for field theories

It is shown that by imposing the relativistic symmetries on the cutoff in field theories, one rules out all known nonperturbative regulators except the point splitting. The relativistic cutoff dynamics is nonlocal in time and thereby unstable, bringing the very existence of relativistic field theory into question. A stable, relativistic regulator is proposed for a scalar field theory model and its semiclassical stability is shown numerically.

Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class

Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is discussed in the case when X is a product of a circle and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral one form on and an integral class in H2(M,ℤ). This case was studied some time ago by V. Mathai, R. Melrose, and I.M. Singer. Our aim is to give an explicit construction for the twisted K-theory classes using a quantum field theory model, in the same spirit as the supersymmetric Wess-Zumino-Witten model is used for constructing (equivariant) twisted K-theory classes on compact Lie groups.