Zeta function regularization of path integrals in curved spacetime

@article{Hawking1977ZetaFR,
  title={Zeta function regularization of path integrals in curved spacetime},
  author={Stephen William Hawking},
  journal={Communications in Mathematical Physics},
  year={1977},
  volume={55},
  pages={133-148}
}
  • S. Hawking
  • Published 1 June 1977
  • Mathematics
  • Communications in Mathematical Physics
This paper describes a technique for regularizing quadratic path integrals on a curved background spacetime. One forms a generalized zeta function from the eigenvalues of the differential operator that appears in the action integral. The zeta function is a meromorphic function and its gradient at the origin is defined to be the determinant of the operator. This technique agrees with dimensional regularization where one generalises ton dimensions by adding extra flat dimensions. The generalized… 
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