Gauged q-Fields

TL;DR

This paper explores the use of an internal Fock space in q-deformed systems to assign physical meaning to transition amplitudes, revealing stringy features in deformed Yang-Mills theories.

Contribution

It introduces a method to interpret q-deformed transition amplitudes via an internal Fock space, linking q-deformation to non-locality and string-like properties in gauge theories.

Findings

Internal Fock space provides a physical interpretation of q-deformed transition amplitudes.

Q-deformation introduces stringy characteristics to Yang-Mills theories.

The approach connects non-locality with internal degrees of freedom in q-systems.

Abstract

The straightforward description of q-deformed systems leads to transition amplitudes that are not numerically valued. To give physical meaning to these expressions without introducing {\it ad hoc} remedies, one may exploit an "internal" Fock space already defined by the q-algebra. This internal space may be interpreted in terms of internal degrees of freedom of the deformed system or alternatively in terms of non-locality. It is shown that the $q$-deformation may give stringy characteristics to a Yang-Mills theory.