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.

Relativistic Theory of the Non-symmetric Field

This chapter attempts to find a measure for the “strength” of a system of field equations, which is determined by the amount of free data consistent with the system. It introduces the infinitesimal displacement field as a necessary remedy in general relativistic theory, as one can no longer form new tensors from a given tensor by simple differentiation and that in such a theory there are much fewer invariant formations. The infinitesimal displacement field replaces the inertial system inasmuch as it makes it possible to compare vectors at infinitesimally close points. After introducing these concepts, the chapter presents a discussion on relativistic field theory.