Functional determinants in higher derivative Lagrangian theories

Abstract

Motivated by the considerable success of alternative theories of gravity, we consider the toy model of a higher derivative Lagrangian theory, which reduces, in the Gaussian approximation, to the Pais–Uhlenbeck oscillator studied in a recent paper by [Hawking and Hertog Phys. Rev. D 65, 103515 (2002)]. Its Euclidean path integral is studied with a certain detail and a pedagogical derivation of the propagator, which makes use of a theorem due to Forman, is consequently proposed.