Some Basic Tools of QFT

TL;DR

This paper provides an educational overview of fundamental quantum field theory tools using a simple cubic model, including explicit calculations and proofs to enhance understanding for undergraduates.

Contribution

It introduces and clearly explains key QFT concepts like functional integrals, generating functions, and Feynman diagrams through explicit calculations in a simple model.

Findings

Explicit calculations of QFT tools in a toy model

Clear proofs of fundamental relations

Enhanced educational clarity for students

Abstract

This work has a methodological nature and is a set of lecture notes for undergraduate students. It is devoted to the study of the basic tools of quantum field theory on the example of the simplest cubic "toy" model. We introduce such concepts as the functional integral, the generating functions, the background field method and the Feynman diagram technique, and also consider relations among them. The model under consideration allows us to perform all the calculations explicitly, which significantly increases the visibility and clarity of the notes. We also provide neat proofs that are usually omitted in standard educational publications.