On Gauge Invariance of the Bosonic Measure in Chiral Gauge Theories

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