Probability current in zero-spin relativistic quantum mechanics

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.