# Renormalization and quantum field theory

@article{Borcherds2010RenormalizationAQ, title={Renormalization and quantum field theory}, author={Richard E. Borcherds}, journal={arXiv: Mathematical Physics}, year={2010} }

The aim of this paper is to describe how to use regularization and renormalization to construct a perturbative quantum field theory from a Lagrangian. We first define renormalizations and Feynman measures, and show that although there need not exist a canonical Feynman measure, there is a canonical orbit of Feynman measures under renormalization. We then construct a perturbative quantum field theory from a Lagrangian and a Feynman measure, and show that it satisfies perturbative analogues of…

## 14 Citations

Causal Perturbative Quantum Field Theory

- Physics
- 2014

This chapter gives a short self-contained and coordinate-free presentation of causal perturbative quantum field theory in the spirit of the Bogomolov-Epstein-Glaser renormalization method, in the…

Noncommutative version of Borcherds' approach to quantum field theory

- Mathematics
- 2015

Richard Borcherds proposed an elegant geometric version of renormalized perturbative quantum field theory in curved spacetimes, where Lagrangians are sections of a Hopf algebra bundle over a smooth…

Species-Theoretic Foundations of Perturbative Quantum Field Theory

- Mathematics
- 2020

We develop an algebraic formalism for perturbative (local) quantum field theory (pQFT) which is based on Joyal's combinatorial species. We show that certain fundamental structures of pQFT are…

An algebraic formulation of the locality principle in renormalisation

- MathematicsEuropean Journal of Mathematics
- 2018

We study the mathematical structure underlying the concept of locality which lies at the heart of classical and quantum field theory, and develop a machinery used to preserve locality during the…

P o S ( F F P 1 4 ) 1 3 4 Noncommutative version of Borcherds ’ approach to quantum field theory

- Mathematics
- 2015

Richard Borcherds proposed an elegant geometric version of ren rmalized perturbative quantum field theory in curved spacetimes, where Lagrangians are sec tions of a Hopf algebra bundle over a smooth…

On the renormalization group of quantum field theory (after R. Bocherds)

- Physics
- 2017

The aim of this thesis is to analyze part of the results presented by R.E. Borcherds in his article on renormalization and quantum field theories. To facilitate this, the first chapter presents the…

General relativity from $p$-adic strings

- Mathematics, Physics
- 2019

For an arbitrary prime number $p$, we propose an action for bosonic $p$-adic strings in curved target spacetime, and show that the vacuum Einstein equations of the target are a consequence of…

On the Holonomic Rank Problem

- Mathematics
- 2013

A tautological system, introduced in \cite{LSY}\cite{LY}, arises as a regular holonomic system of partial differential equations that govern the period integrals of a family of complete intersections…

Renormalization of quantum field theory on curved space-times, a causal approach

- Mathematics, Physics
- 2013

Le sujet de la these est la construction d'une theorie perturbative des champs quantiques en interaction sur un espace-temps courbe, suivant un point de vue concu par Stueckelberg et Bogoliubov et…

Complex powers of analytic functions and meromorphic renormalization in QFT

- Mathematics
- 2015

In this article, we study functional analytic properties of the meromorphic families of distributions $(\prod_{i=1}^p (f_j+i0)^{\lambda_j})_{(\lambda_1,\dots,\lambda_p) \in \mathbb{C}^p}$ using…

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