On Gauge Invariance of the Bosonic Measure in Chiral Gauge Theories

Gauge invariance of the measure associated with the gauge field is usually taken for granted, in a general gauge theory. We furnish a proof of this invariance, within Fujikawa's approach. To stress the importance of this fact, we briefly review gauge anomaly cancellation as a consequence of gauge invariance of the bosonic measure and compare this cancellation to usual results from algebraic renormalization, showing that there are no potential inconsistencies. Then, using a path integral argument, we show that a possible Jacobian for the gauge transformation has to be the identity operator, in the physical Hilbert space. We extend the argument to the complete Hilbert space by a direct calculation.

Automated summary

This paper provides a proof of the gauge invariance of the measure associated with the gauge field, and highlights the importance of this fact by showing the effective cancellation of gauge anomalies. Through path integral arguments and direct calculations, it is demonstrated that the Jacobian for gauge transformations must be the identity operator in the physical Hilbert space.