Relativistic Quantum Mechanics of Spin-0 and Spin-1 Bosons

Abstract

It is shown that below the threshold of pair creation, a consistent quantum mechanical interpretation of relativistic spin-0 and spin-1 particles (both massive and massless) is possible based on the Hamiltonian-Schrödinger form of the first-order Kemmer equation together with a first-class constraint. The crucial element is the identification of a conserved four-vector current associated with the equation of motion, whose time component is proportional to the energy density which is constrained to be positive definite for all solutions. Consequently, the antiparticles must be interpreted as positive-energy states traveling backward in time. This also makes it possible to define hermitian position operators with localized eigensolutions (δ-functions) as well as Bohman trajectories for bosons. The exact theory is obtained by "second quantization" and is mathematically completely equivalent to conventional quantum field theory. The classical field emerges in the high mean number limit of coherent states of the exact theory. The formalism provides a new basis for computing tunneling times for photons and chaotic phenomena in optics.