Zero mass field quantization and Kibble's long-range force criterion for the Goldstone theorem
The central theme of the dissertation is an investigation of the long-range force criterion used by Kibble in his discussion of the Goldstone Theorem. This investigation is broken up into the following sections: I. Introduction. Spontaneous symmetry breaking, the Goldstone Theorem and the conditions under which it holds are discussed. II. Massless Wave Expansions. In order to make explicit calculations of the operator commutators used in applying Kibble's criterion, it is necessary to work out the operator expansions for a massless field. Unusual results are obtained which include operators corresponding to classical macroscopic field modes. III. The Kibble Criterion for Simple Models Exhibiting Spontaneously Broken Symmetries. The results of the previous section are applied to simple models with spontaneously broken symmetries, namely, the real scalar massless field and the Goldstone model without gauge coupling. IV. The Higgs Mechanism in Classical Field Theory. It is shown that the Higgs Mechanism has a simple interpretation in terms of classical field theory, namely, that it arises from a derivative coupling term between the Goldstone fields and the gauge fields. V. The Higgs Mechanism and Kibble's Criterion. This section draws together the material discussed in sections II to IV. Explicit calculations are made to evaluate Kibble's criterion on a Goldstone-Higgs type of model in the Coulomb gauge. It is found, as expected, that the criterion is not met, but not for reasons relating to the range of the mediating force. By referring to the findings of sections III and IV, it is concluded that the common denominator underlying both the Higgs Mechanism and the failure of Kibble's criterion is a structural aspect of the field equations: derivative coupling between fields.
- Research Organization:
- Boston Univ., MA (USA). Graduate School
- OSTI ID:
- 5230633
- Country of Publication:
- United States
- Language:
- English
Similar Records
Quark confinement and the evasion of Goldstone's theorem in 1 + 1 dimensions
Is there spontaneous symmetry breaking in gauge theories with the Higgs-- Kibble mechanism.
Related Subjects
645400 -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
COUPLING
DISTANCE
ELEMENTARY PARTICLES
FIELD THEORIES
GOLDSTONE BOSONS
HIGGS MODEL
INTERACTION RANGE
MATHEMATICAL MODELS
PARTICLE MODELS
POSTULATED PARTICLES
QUANTUM FIELD THEORY
SYMMETRY BREAKING