Introduction to Renormalisation

TL;DR

This paper provides an accessible introduction to the renormalisation group concepts in quantum field theory, focusing on scalar fields and avoiding complex topics like infinities, symmetries, and gauge fields.

Contribution

It offers a simplified, self-contained overview of renormalisation group ideas tailored for beginning graduate students without requiring prior quantum field theory knowledge.

Findings

Standard results derived without infinities

Clarification of renormalisation concepts in scalar field context

Connection to statistical field theory briefly mentioned

Abstract

These are introductory lecture notes aimed at beginning graduate students covering fundamental concepts and ideas behind the renormalisation group. Our main goal is to motivate it and then explore its consequences, in the context of quantum field theory. We shall reproduce the standard results without needing any mention of cancellation of infinities. To keep the story simple and compact, we'll ignore the role of symmetry in this game. We'll also restrict to scalar fields, and not mention neither fermions nor gauge fields. Moreover, we'll only briefly mention the connection with statistical field theory. Knowledge of quantum mechanics and special relativity is essential. Prior knowledge of quantum field theory is not required, however, this is not designed to be an introduction to QFT, so it may not be the most pedagogical way to introduce the topic. Previous familiarity with path integrals is also not assumed.