Multi-Loop Zeta Function Regularization and Spectral Cutoff in Curved Spacetime

Understand

We emphasize the close relationship between zeta function methods and arbitrary spectral cutoff regularizations in curved spacetime.

• This yields, on the one hand, a physically sound and mathematically rigorous justification of the standard zeta function regularization at one loop and, on the other hand, a natural generalization of this method to higher loops.
• In particular, to any Feynman diagram is associated a generalized meromorphic zeta function.
• For the one-loop vacuum diagram, it is directly related to the usual spectral zeta function.