A derivation of the classical limit of quantum mechanics and quantum electrodynamics
Instead of regarding the classical limit as the h {yields} 0, an alternative view based on the physical interpretation of the elements of the density matrix is proposed. According to this alternative view, taking the classical limit corresponds to taking the diagonal elements and ignoring the off-diagonal elements of the density matrix. As illustrations of this alternative approach, the classical limits of quantum mechanics and quantum electrodynamics are derived. The derivation is carried out in two stages. First, the statistical classical limit is derived. Then with an appropriate initial condition, the deterministic classical limit is obtained. In the case of quantum mechanics, it is found that the classical limit of Schroedinger's wave mechanics is at best statistical, i.e., Schroedinger's wave mechanics does not reduce to deterministic (Hamilton's or Newton's) classical mechanics. In order to obtain the latter, it is necessary to start out initially with a mixture at the level of statistical quantum mechanics. The derivation hinges on the use of the Feynman path integral rigorously defined with the aid of nonstandard analysis. Nonstandard analysis is also applied to extend the method to the case of quantum electrodynamics. The fundamental decoupling problem arising form the use of Grassmann variables is circumvented by the use of c-number electron fields, but antisymmetrically tagged. The basic classical (deterministic) field equations are obtained in the classical limit with appropriate initial conditions. The result raises the question as to what the corresponding classical field equations obtained in the classical limit from the renormalized Lagrangian containing infinite counterterms really mean.
- Research Organization:
- Purdue Univ., Lafayette, IN (USA)
- OSTI ID:
- 5074454
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
QUANTUM ELECTRODYNAMICS
MATHEMATICAL MODELS
QUANTUM MECHANICS
CALCULATION METHODS
DENSITY MATRIX
DERIVATIZATION
FIELD EQUATIONS
FIELD THEORIES
CHEMICAL REACTIONS
ELECTRODYNAMICS
EQUATIONS
MATRICES
MECHANICS
QUANTUM FIELD THEORY
645400* - High Energy Physics- Field Theory
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics