The Intrinsic Angular - Momentum of Particles and the Resolution of the Spin-Statistics Theorem

TL;DR

This work addresses the long-standing Spin-Statistics Connection (SSC) puzzle by embedding quantum mechanics in Weyl Integrable Quantum Mechanics (WIQM), which augments standard QM with a conserved intrinsic angular momentum $s_\zeta$ (intrinsic helicity) and a kinematic constraint that permits rotation about a particle's proper axis only in one sense. By extending the configuration space to $E_3\times SO(3)$ and employing Weyl's integrable geometry, the authors derive a scalar wave function $\Psi=e^{is\gamma}\Phi_s$ whose internal spinor content $\Phi_s$ encodes the usual spin degrees of freedom, with $s$ constrained to integer or half-integer values by $SO(3)$ representations. Exchanging identical particles induces a $2\pi$ shift in the sum of the Euler angles $\gamma_a$, yielding a phase factor $(-1)^{2ks}$ that must be compensated by the spinor part, and leading to the familiar (anti)symmetrization of the many-body state: $\psi^{\sigma_1,...,\sigma_N}=\frac{1}{N!}\sum_{\alpha}(-1)^{2s}p_{\alpha}[\psi_1^{\sigma_1}\cdots\psi_N^{\sigma_N}]$. Consequently, WIQM provides a nonrelativistic derivation of SSC without quantum field theory, while treating bosons and fermions on the same footing at the level of $\Psi$, with spin-statistics arising from rotational properties and the IAM. This framework promises a more complete quantum theory, potentially extendable to relativistic regimes in future work.

Abstract

The traditional Standard Quantum Mechanics (SQM) theory is unable to solve the Spin-s problem, i.e., to justify the utterly important "Pauli Exclusion Principle". A complete and straightforward solution of the Spin-Statistics problem is presented based on the "Weyl Integrable Quantum Mechanics" (WIQM) theory. This theory provides a Weyl-gauge invariant formulation of the Standard Quantum Mechanics and reproduces successfully, with no restrictions, the full set of the quantum mechanical processes, including the formulation of Dirac's or Schrödinger's equation, of Heisenberg's uncertainty relations, and of the nonlocal EPR correlations. etc. When the Weyl Integrable Quantum Mechanics is applied to a system made of many identical particles with spin, an additional constant property of all elementary particles enters naturally into play: the "intrinsic helicity", or the "intrinsic angular - momentum". This additional particle property, not considered by Standard Quantum Mechanics, determines the correct Spin-Statistics Connection (SSC) observed in Nature. All this leads to the consideration of a novel, most complete (in the EPR sense) quantum mechanical theory.