Riemann-Zeta-Regularisation of Feynman Path Integrals

Abstract

The Feynman Propagator of a charged particle confined to an anisotropic Harmonic Oscillator potential and moving in a crossed electromagnetic field is calculated in a conceptually new way. The calculation is based on the expansion of the path variable into a complex Fourier series. The path integral then becomes an infinite product of Gaussian integrals. This product is divergent. It turns out that we can regularize this product by using the zeta-function. It is a remarkable fact that the zeta-function is so well suited as a regularizator for divergent path integrals.