Quantum Groups and Field Theory

TL;DR

This paper explores how deforming symmetries in field theories using quantum groups introduces new degrees of freedom, resulting in a richer, non-local structure with potential observable differences from standard theories.

Contribution

It provides a theoretical framework for understanding how quantum group deformations affect field theories, revealing new spectra and non-local features.

Findings

Energy levels acquire fine structure.

Massive particles exhibit stringlike spectra.

Presence of two sectors with different observability prospects.

Abstract

When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If the symmetry of a field theory is deformed in this way, the enlarged state space will again describe additional degrees of freedom, and the energy levels will acquire fine structure. The massive particles will have a stringlike spectrum lifting the degeneracy of the point-particle theory, and the resulting theory will have a non-local description. Theories of this kind naturally contain two sectors with one sector lying close to the standard theory while the second sector describes particles that should be more difficult to observe.