Yang-Mills analogues of the Immirzi ambiguity

We show that the somewhat controversial “Immirzi ambiguity” of the Ashtekar-like formulation of canonical quantum gravity has strong similarities with other ambiguities that appear in Yang-Mills theories, such as the $\theta$ ambiguity. This clarifies the role of the ambiguities. We also discuss other ambiguities in the Maxwell case, and the implications for the loop quantization of these theories.