Some uses of $\zeta-$regularization in quantum gravity and cosmology

TL;DR

This paper reviews how zeta-function regularization is used as a mathematical tool in quantum field theory, quantum gravity, and cosmology, particularly for calculating vacuum energy contributions to the cosmological constant.

Contribution

It provides a concise overview of zeta-regularization applications across various areas of theoretical physics, highlighting its versatility and importance.

Findings

Zeta-regularization aids in quantum field theory in curved spacetime.

It is useful in quantum gravity models across different dimensions.

The method helps estimate vacuum energy contributions to the cosmological constant.

Abstract

This is a short guide to some uses of the zeta-function regularization procedure as a a basic mathematical tool for quantum field theory in curved space-time (as is the case of Nambu-Jona-Lasinio models), in quantum gravity models (in different dimensions), and also in cosmology, where it appears e.g. in the calculation of possible `contributions' to the cosmological constant coming through manifestations of the vacuum energy density. Part of this research was carried out in fruitful and enjoyable collaboration with people from Tomsk State Pedagogical University.