Spectral problems from quantum field theory

TL;DR

This paper explores the role of spectral functions of differential operators in quantum field theory, discussing consistency conditions, boundary problems, and recent developments in the field.

Contribution

It introduces new spectral and boundary value problems arising from quantum field theory and string theory, along with formulation of necessary consistency conditions.

Findings

Identification of spectral functions in quantum field contexts

Formulation of consistency conditions for operators and boundary conditions

Review of modern developments and new spectral problems

Abstract

We describe how spectral functions of differential operators appear in the quantum field theory context. We formulate consistency conditions which should be satisfied by the operators and by the boundary conditions. We review some modern developments in quantum field theory and strings and show which new spectral and boundary value problems arise.