No Drama Quantum Theory? A Review

TL;DR

This review explores a simplified formulation of quantum theory where matter fields are eliminated, leading to potentially more intuitive, classical-like models consistent with experimental data and offering new perspectives on quantum interpretations.

Contribution

The paper demonstrates that matter fields in quantum electrodynamics can be algebraically eliminated, resulting in equations describing electromagnetic fields alone, which may serve as 'no drama' quantum theories.

Findings

Matter fields can be algebraically eliminated in scalar and spinor electrodynamics.

The resulting equations describe electromagnetic field dynamics independently.

Embedded models are consistent with experimental data and resemble classical electrodynamics.

Abstract

Schr\"{o}dinger (Nature, v.169, 538 (1952)) noted that the complex matter field in the Klein-Gordon equation can be made real by a gauge transform, although charged fields are believed to require complex functions. Surprisingly, the result can be extended to the Dirac equation: three complex components of the Dirac spinor function can be algebraically eliminated, and the remaining component can be made real by a gauge transform. Therefore, the Dirac equation is generally equivalent to one fourth-order partial differential equation for one real function (A. Akhmeteli, J. Math. Phys. v.52, 082303 (2011)). These results both belong in textbooks and can be used for development of new efficient methods of quantum chemistry. The matter field can be algebraically eliminated both in scalar electrodynamics and in spinor electrodynamics in a certain gauge. The resulting equations describe independent dynamics of the electromagnetic field, which permits mathematical simplification and can be useful for interpretation of quantum theory. For example, in the Bohm interpretation, the electromagnetic field can replace the wave function as the guiding field. It is also shown that for these equations, generalized Carleman embedding generates systems of linear equations in the Hilbert space, which look like second-quantized theories and are equivalent to the original nonlinear systems on the set of solutions of the latter. Thus, the relevant local realistic models can be embedded into quantum field theories. These models are equivalent to scalar electrodynamics and spinor electrodynamics, so they correctly describe a large body of experimental data. Although they may need some modifications for better agreement with experiments, they may be of great interest as "no drama quantum theories", as simple (in principle) as classical electrodynamics. Possible issues with the Bell theorem are discussed.