Weyl-gauge invariant proof of the Spin-Statistics Theorem

TL;DR

This paper extends a nonrelativistic proof of the spin-statistics connection to a relativistic, curved spacetime setting using Weyl gauge invariance and group theory, avoiding quantum field operators.

Contribution

It provides a relativistic, gauge-invariant proof of the Spin-Statistics Theorem based solely on symmetry considerations and intrinsic helicity conservation.

Findings

Proof applies to curved spacetime scenarios.

Relativistic approach emphasizes group theory and helicity.

Avoids quantum field operators in the proof.

Abstract

The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important \qo{Pauli Exclusion Principle} but by the adoption of the complex standard relativistic quantum field theory. In a recent paper (Ref. [1]) we presented a proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the \qo{Conformal Quantum Geometrodynamics}. In the present paper, by the same theory the proof of the Spin-Statistics Theorem is extended to the relativistic domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the Standard Quantum Mechanics, which determines the correct spin-statistics connection observed in Nature [1]. The present proof of the Spin-Statistics Theorem is simpler than the one presented in Ref. [1], because it is based on symmetry group considerations only, without having recourse to frames attached to the particles.