REFLECTIONS ON THE SIMULTANEOUS EXISTENCE OF THE HEISENBERG AND INTERACTION PICTURES IN PRACTICAL PRE-THEORIES OF Q.E.D. (QED, QUANTUM ELECTRODYNAMICS)

MARVIN CARROLL YOAKAM, Purdue University

Abstract

The purpose of this thesis is to investigate the possibility of simultaneously incorporating both Lorentz invariance and a special gauge invariance among Boson fields satisfying Proca-like commutators and gauge conditions (including Proca, Feynman, Yennie, Landau, and Coester Gauge choices for the commutators) as a stationary condition in both the interaction and Heisenberg pictures for Lagrangian formulations of second-quantized neutral vector-meson theories (which include regularization by the auxillary-field method) before the regularization is removed. This approach, if ultimately successful, will demonstrate that Lorentz invariance and gauge invariance can be included as internal symmetries of a regularized form of quantum electrodynamics. A simple interaction operator (which reflects current methodology for accommodating infrared and ultraviolet divergences and which provides an integrable Schrodinger equation) was augmented with frame-dependent interactions (introduced by generalizations of the Fermi operator) to fix the subsidiary conditions of Proca-like Boson fields as stationary conditions in both the Heisenberg and Interaction pictures. It was demonstrated that, with spinor mass-counterterms but without Boson mass-counterterms, a generalization of the method of Coester and Stuckelberg to reduce the usual forms of the Proca-like field interactions to the simpler Coester interaction is applicable. Therefore, the choice of the interaction operator is more general than its surface appearance would indicate. Under the same restrictions, it was shown that a simple generalization of the Fermi operator will provide stationary gauge conditions for the Proca-like Boson operators, but that the requirement of limited-gauge-invariance in both the Heisenberg and interaction pictures removes the ambiguity usually associated with the Fermi operator. In the presence of the Boson mass counterterms, it was shown that the subsidiary conditions are, in general, no longer stationary in the Heisenberg picture. Equations are presented which would be satisfied by an extension of the Fermi operator chosen to reestablish the gauge conditions as stationary conditions in both pictures.

Degree

Ph.D.

Subject Area

Particle physics

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