Lectures on differentials, generalized differentials and on some examples related to theoretical physics

TL;DR

This paper surveys the theory of differential modules, complexes, and their generalizations, highlighting applications in physics, especially gauge systems and higher spin fields, with explanations of BRS methods.

Contribution

It introduces the theory of N-differential modules and complexes and explores their applications in physics, particularly in gauge theories and higher spin fields.

Findings

Analysis of N-complexes in higher spin gauge theories

Application of BRS methods to constrained systems

Examples from physics illustrating differential module theory

Abstract

These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of $N$-differential modules and $N$-complexes. Several applications and examples coming from physics are discussed. The commun feature of these physical applications is that they deal with the theory of constrained or gauge systems. In particular different aspects of the BRS methods are explained and a detailed account of the $N$-complexes arising in the theory of higher spin gauge fields is given.