Quantum theory of non-abelian differential forms and link polynomials

TL;DR

This paper develops a topological quantum field theory for non-abelian differential forms, aiming to describe polynomial invariants of higher-dimensional links using a covariant, non-perturbative approach.

Contribution

It introduces a novel quantum field theory framework for non-abelian differential forms and derives skein relations via a covariant path-integral approach.

Findings

Path-integral representation of the partition function obtained.

Quasi-monodromy matrix formally derived.

Skein relations established for link invariants.

Abstract

A topological quantum field theory of non-abelian differential forms is investigated from the point of view of its possible applications to description of polynomial invariants of higher-dimensional two-component links. A path-integral representation of the partition function of the theory, which is a highly on-shell reducible system, is obtained in the framework of the antibracket-antifield formalism of Batalin and Vilkovisky. The quasi-monodromy matrix, giving rise to corresponding skein relations, is formally derived in a manifestly covariant non-perturbative manner.