Spin in quantum field theory

TL;DR

This paper explores the concept of spin in quantum field theory by deriving the spin-statistics connection from quantum mechanics, discussing path integrals for spin without spinors, and quantizing spin via path integrals without anticommuting variables.

Contribution

It presents a novel approach to understanding spin in quantum field theory by deriving key concepts from quantum mechanics and developing path integral methods that avoid spinors and anticommuting variables.

Findings

Derived the spin-statistics connection in quantum mechanics without relativity.

Developed path integral formulations for spin without using spinors.

Quantized spin using path integrals without anticommuting variables.

Abstract

I introduce spin in field theory by emphasizing the close connection between quantum field theory and quantum mechanics. First, I show that the spin-statistics connection can be derived in quantum mechanics without relativity or field theory. Then, I discuss path integrals for spin without using spinors. Finally, I show how spin can be quantized in a path-integral approach, without introducing anticommuting variables.