INEQUIVALENT HAMILTONIAN FORMALISMS IN ELECTRODYNAMICS

Journal Article · Wed May 15 00:00:00 EDT 1963 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.130.1595· OSTI ID:4693170

Schwartz, M

BS>In treating the electric dipole approximation of a charged particle undergoing self-interaction, it is shown how, in the cases of a charged free particle and a charged oscillator, the same equations of motion may be derived from two inequivalent Hamiltonian formalisms. The first formalism is the Dirac formalism of Schiller and Schwartz, which must be satisfied by all configuration space solutions generated by the total Hamiltonian. In order to ensure that the configuration space solutions are consistent with the latter formalism, the constraints must be recognized as imposing modifications on the commutation rules satisfied by averaged field variables. While the first formalism is general, the second formalism can be constructed only after solutions expressed in terms of a Fourier decomposition of the radiation fleld are obtained. The second formalism is an interaction picture formalism where the radiation field part of the total Hamiltonian is the generator of time translations. The latter formalism is used to give a new derivation of Kramers' integral for the zero-point level shift of an oscillator. Some asymptotic boundary conditions and a recent paper by Sokolov and Lysov are also discussed. (auth)

• Research Organization: Syracuse Univ., N.Y.; and Adelphi Coll., Garden City, N.Y.
• NSA Number: NSA-17-022352
• OSTI ID: 4693170
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 130; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BOUNDARY CONDITIONS
CHARGED PARTICLES
CONFIGURATION
DIFFERENTIAL EQUATIONS
DIPOLES
DIRAC RADIATION THEORY
ELECTRODYNAMICS
ENERGY LEVELS
EQUATIONS
FOURIER ANALYSIS
HAMILTONIAN
INTERACTIONS
MATHEMATICS
MOTION
OSCILLATIONS
PHYSICS
RADIATIONS
SPECTRAL SHIFT