
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…
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