# Spin and Statistics and First Principles

## TL;DR

This paper discusses the foundational principles of the Spin-Statistics Theorem in quantum field theory, emphasizing its derivation from local observable quantities and exploring its applicability to various particle types and theories.

## Contribution

It provides a first-principles derivation of the Spin-Statistics Theorem within Local Quantum Theory and discusses its potential extensions and limitations.

## Key findings

- Spin-Statistics Theorem derived from first principles
- Existence of a unique algebra of local field operators
- Applicability to massive particles with finite degeneracy

## Abstract

It was shown in the early Seventies that, in Local Quantum Theory (that is the most general formulation of Quantum Field Theory, if we leave out only the unknown scenario of Quantum Gravity) the notion of Statistics can be grounded solely on the local observable quantities (without assuming neither the commutation relations nor even the existence of unobservable charged field operators); one finds that only the well known (para)statistics of Bose/Fermi type are allowed by the key principle of local commutativity of observables. In this frame it was possible to formulate and prove the Spin and Statistics Theorem purely on the basis of First Principles. In a subsequent stage it has been possible to prove the existence of a unique, canonical algebra of local field operators obeying ordinary Bose/Fermi commutation relations at spacelike separations. In this general guise the Spin - Statistics Theorem applies to Theories (on the four dimensional Minkowski space) where only massive particles with finite mass degeneracy can occur. Here we describe the underlying simple basic ideas, and briefly mention the subsequent generalisations; eventually we comment on the possible validity of the Spin - Statistics Theorem in presence of massless particles, or of violations of locality as expected in Quantum Gravity.