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International Journal of Quantum Chemistry

Quantum classical correspondence in nonrelativistic electrodynamics

Burke Ritchie, Charles A. Weatherford

Published Jan 1, 1999• 0 citations
Publisher

Abstract

A form of classical electrodynamic field exists which gives exact agreement with the operator field of quantum electrodynamics (QED) for the Lamb shift of a harmonically bound point electron. Here it is pointed out that this form of classical theory, with its physically acceptable interpretation, is the result of an unconventional resolution of a mathematically ambiguous term in classical field theory. Finally, a quantum classical correspondence principle is shown to exist in the sense that the classical field and expectation value of the QED operator field are identical, if retardation is neglected in the latter. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 655–658, 1999

DOI
10.1002/(sici)1097-461x(1999)75:4/5<655::aid-qua32>3.0.co;2-v

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A form of classical electrodynamic field exists which gives exact agreement with the operator field of quantum electrodynamics (QED) for the Lamb shift of a harmonically bound point electron. Here it is pointed out that this form of classical theory, with its physically acceptable interpretation, is the result of an unconventional resolution of a mathematically ambiguous term in classical field theory. Finally, a quantum classical correspondence principle is shown to exist in the sense that the classical field and expectation value of the QED operator field are identical, if retardation is neglected in the latter. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 655–658, 1999
We use a self-field approach to quantum electrodynamics (QED) to show how one may obtain spontaneous emission and the Lamb shift in a two-level atom without second quantization of the radiation field. In addition, we compare the self-field formalism to that of the neoclassical theory of electrodynamics advanced by Crisp and Jaynes [Phys. Rev. 179, 1253 (1969)]. We show that the neoclassical model can be obtained from the self-field approach used here, but that the two are not equivalent. In particular, the self-field approach appears to give a more complete description of radiative processes. Finally, we show that the neoclassical theory's prediction of a nonexponential ``chirruped'' decay is most likely a mathematical artifact of the improper application of the superposition principle in a nonlinear model where such a principle does not hold. A correct treatment with self-field QED yields the usual exponential decay dynamics.
New excitation operators which have perfect bosonic symmetry are constructed for many-electron wave functions by regarding the system of many electrons as that of many species of bosons. Any electronic configurations can be generated by the new bosonic “void” operators. A coherent state is constructed with the bosonic operators and is adopted as a trial function for the time-dependent variational principle. The equation of motion which has exactly the same form as Hamilton's equation in classical mechanics is obtained with the complex variational parameters, the number of which is equal to the number of electrons. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 71–75, 1998
Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as an more fundamental theory, but as an upgrade of classical electrodynamics, which permits an extension of classical theory to the description of phenomena that, while being related to the conceptual framework of the classical theory, cannot be addressed from the classical theory.
Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as a more fundamental theory, but as an upgrade of classical electrodynamics, which permits an extension of classical theory to the description of phenomena that, while being related to the conceptual framework of the classical theory, cannot be addressed from the classical theory.
A correspondence of classical to quantum physics studied by Schrö\-dinger and Ehrenfest applies without the necessity of technical conjecture that classical observables are associated with Hermitian Hilbert space operators. This correspondence provides appropriate nonrelativistic classical interpretations to realizations of relativistic quantum physics that are incompatible with the canonical formalism. Using this correspondence, Newtonian mechanics for a 1/r1/r1/r potential provides approximations for the dynamics of nonrelativistic classical particle states within unconstrained quantum field theory (UQFT).