Numbers and Functions in Quantum Field Theory

TL;DR

This paper reviews recent advances in number theory and complex functions relevant to quantum field theory, applying these to compute key renormalization functions in $\

Contribution

It introduces novel applications of number theory and complex functions to high-loop calculations in quantum field theory.

Findings

Calculated $eta$, $\gamma$, $\gamma_m$ functions up to seven loops.

Connected number theory with quantum field renormalization.

Enhanced understanding of mathematical structures in quantum field calculations.

Abstract

We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, $\gamma_m$ of dimensionally regularized $\phi^4$ theory in the minimal subtraction scheme up to seven loops.