Matthias Ludewig
It is "well-known" in quantum field theories that the values of certain path integrals are given by associated zeta-determinants "up to a multiplicative constant". What is usually meant is that one can only calculate the ratio of path integrals by the ratio of zeta functions. The "relativity principle" for zeta functions in turn relates this to usual Hilbert space determinants. We give a rigorous meaning to all these statements and show how finite-dimensional approximation of path integrals can be used to prove them.
