Heisenberg relations in the general case

TL;DR

This paper generalizes the derivation of Heisenberg relations using group representations, including in the fibre bundle framework, and illustrates the results with Poincare group transformations.

Contribution

It extends Heisenberg relations derivation to a broad setting involving group representations and fibre bundles, providing a more general theoretical framework.

Findings

Heisenberg relations derived for general group-induced transformations.

Inclusion of fibre bundle approach broadens the applicability.

Illustration with Poincare group demonstrates practical relevance.

Abstract

The Heisenberg relations are derived in a quite general setting when the field transformations are induced by three representations of a given group. They are considered also in the fibre bundle approach. The results are illustrated in a case of transformations induced by the Poincare group.