Quantum theory of particles of indefinite mass: Spin- 1/2

Abstract

The quantum theory of particles of indefinite mass investigated earlier by Hostler [J. Math. Phys. 21, 2461 (1980); 22, 2307 (1981)] is adapted to apply to spin- 1/2 particles. The proposed wave equation is { 1/2 Π⋅(1+iσ)⋅Π+(1/i)(∂/∂λ)} φ=0, Πμ=pμ−eAμ, in which φ is a 2×1 Pauli spinor and σ is a spin tensor whose Lorentz components are 2×2 Pauli spin matrices. Particle scattering by an external c-number static field is computed within the framework of the new formalism, and agreement with the known physics of a charged spin- 1/2 particle is obtained for this special case.