Violation of the phase space general covariance as a diffeomorphism anomaly in quantum mechanics

Understand

We consider a topological quantum mechanics described by a phase space path integral and study the 1-dimensional analog for the path integral representation of the Kontsevich formula.

• We see that the naive bosonic integral possesses divergences, that it is even naively non-invariant and thus is ill-defined.
• We then consider a super-extension of the theory which eliminates the divergences and makes the theory naively invariant.
• This super-extension is equivalent to the correct choice of measure and was discussed in the literature.