Transformation laws of the components of classical and quantum fields and Heisenberg relations

TL;DR

This paper reviews the transformation laws of classical and quantum fields from standard and fibre bundle perspectives, and applies these to derive Heisenberg relations, especially under Poincaré group transformations.

Contribution

It introduces a general framework for deriving Heisenberg relations using fibre bundle methods, extending traditional approaches.

Findings

Transformation laws are derived from both standard and fibre bundle viewpoints.

Heisenberg relations are obtained in a general setting, including fibre bundle formalism.

Results are exemplified with Poincaré group transformations.

Abstract

The paper recalls and point to the origin of the transformation laws of the components of classical and quantum fields. They are considered from the "standard" and fibre bundle point of view. The results are applied to the derivation of the Heisenberg relations in quite general setting, in particular, in the fibre bundle approach. All conclusions are illustrated in a case of transformations induced by the Poincar\'e group.