Analytic continuation of the Hurwitz Zeta Function with physical application

Abstract

A new formula relating the analytic continuation of the Hurwitz zeta function to the Euler gamma function and a polylogarithmic function is presented. In particular, the values of the first derivative of the real part of the analytic continuation of the Hurwitz zeta function for even negative integers and the imaginary one for odd negative integers are explicitly given. The result can be of interest both on mathematical and physical side, because we are able to apply our new formulas in the context of the Spectral Zeta Function regularization, computing the exact pair production rate per space-time unit of massive Dirac particles interacting with a purely electric background field.

Replaced version, minor changes. 9 pages, to be published in J. Math. Phys

References in corpus (7)

• Quantum Fields and Extended Objects in Space-Times with Constant Curvature Spatial Section
• Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part I
• Analytic results for the effective action
• Local $\zeta$-function techniques vs point-splitting procedure: a few rigorous results
• Effective Action - A Convergent Series - of QED
• Effective action for Dirac spinors in the presence of general uniform electromagnetic fields
• Effective action for QED_4 through zeta function regularization

Cited by in corpus (1)

• On the Hurwitz Zeta Function of Imaginary Second Argument