Probability current in zero-spin relativistic quantum mechanics

TL;DR

This paper demonstrates that the antisymmetric spinor tensor representation for spin-0 relativistic particles yields a positive probability current, offering a new one-particle framework analogous to the spin-1/2 case, distinct from Klein-Gordon theory.

Contribution

It introduces a novel representation for spin-0 particles that provides a positive-definite probability current, differing from Klein-Gordon and enabling potential new quantum field interactions.

Findings

Provides a conserved, positive-definite probability current for spin-0 particles.

Establishes a one-particle Hilbert space framework analogous to spin-1/2.

Shows the formulation is inequivalent to Klein-Gordon for interacting particles.

Abstract

We show that the antisymmetric spinor tensor representation of spin-0 relativistic quantum mechanics provides a conserved current with positive definite timelike component, interpretable as probability density. The construction runs in complete analogy to the spin-1/2 case, and provides an analogously natural one-particle Hilbert space description for spin 0. Except for the free particle, the obtained formulation proves to be inequivalent to the one based on the Klein--Gordon equation. The second quantized version may lead to new field theoretical interaction terms for zero-spin particles.