On Peculiarities and Pit Falls in Path Integrals

TL;DR

This paper discusses the challenges and limitations of defining path integrals in high-dimensional systems, emphasizing the need for caution and the speculative nature of certain models beyond four dimensions.

Contribution

It provides a critical perspective on the mathematical and conceptual difficulties in extending path integrals to higher dimensions.

Findings

Path integrals are rigorously defined only in low-dimensional systems.

High-dimensional models often require speculative approaches.

The paper offers a perspective on the limitations of current methods.

Abstract

Path integrals can be rigorously defined only in low dimensional systems where the small distance limit can be taken. Particularly non-trivial models in more than four dimensions can only be handled with considerable amount of speculation. In this lecture we try to put these various aspects in perspective.