No drama quantum theory?

Abstract

Is it possible to offer a "no drama" quantum theory? Something as simple (in principle) as classical electrodynamics - a theory described by a system of partial differential equations in 3+1 dimensions, but reproducing unitary evolution of a quantum field theory in the configuration space? The following results suggest an affirmative answer: 1. The scalar field can be algebraically eliminated from scalar electrodynamics; the resulting equations describe independent evolution of the electromagnetic field. 2. After introduction of a complex 4-potential (producing the same electromagnetic field as the standard real 4-potential), the spinor field can be algebraically eliminated from spinor electrodynamics; the resulting equations describe independent evolution of the electromagnetic field. 3. The resulting theories for the electromagnetic field can be embedded into quantum field theories. Another fundamental result: in a general case, the Dirac equation is equivalent to a 4th order partial differential equations for just one component, which can be made real by a gauge transform. Issues related to the Bell theorem are discussed.