Gauge Theories under Incorporation of a Generalized Uncertainty Principle

Understand

There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale.

• A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation.
• If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative.
• This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self interaction of the gauge field.