Quantum field theory of particles of indefinite mass. II. An electromagnetic model

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Abstract
A new model of the electromagnetic field is postulated. The model is designed within the conceptual framework of the quantum field theory of particles of indefinite mass. The model is built around an interaction Lagrangian of the type ℒI = (1/2) ρV−JμAμ, where (Jμ;ρ) is a conserved c-number 5-current. A gauge invariance principle is thereby built into the theory. The object (1/2) V is a new 5th component of the vector potential. Due to the use of the new evolution parameter τ, second quantization in the Lorentz gauge ∂μAμ = 0 parallels Coulomb gauge quantization in ordinary quantum electrodynamics. The Hamiltonian of the free electromagnetic field is negative definite and has the physical interpretation of minus half the sum of the squares of the masses of the photons present. The inner product in Hilbert space is not positive definite, spacelike states with timelike polarization having negative norm.

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