# Large scale analytic calculations in quantum field theories

## TL;DR

This paper surveys the mathematical structures and calculation methods used in high-order perturbative quantum field theory, focusing on zero- and single-scale quantities and their associated function spaces.

## Contribution

It provides a comprehensive overview of the mathematical frameworks and techniques for perturbative calculations in relativistic quantum field theories.

## Key findings

- Detailed classification of function spaces used in calculations
- Analysis of mathematical structures underlying perturbative methods
- Overview of calculation techniques for higher-order corrections

## Abstract

We present a survey on the mathematical structure of zero- and single scale quantities and the associated calculation methods and function spaces in higher order perturbative calculations in relativistic renormalizable quantum field theories.