Austerity and geometric structure of field theories
The relation between the austerity idea and the geometric structure of the three basic field theories - electrodynamics, Yang-Mills theory, and general relativity - is studied. One of the most significant manifestations of the austerity idea in field theories is thought to be expressed by the boundary of a boundary principle (BBP). The BBP says that almost all content of the field theories can be deduced from the topological identity of delta dot produced with delta = 0 used twice, at the 1-2-3-dimensional level (providing the homogeneous field equations), and at the 2-3-4-dimensional level (providing the conservation laws for the source currents). There are some difficulties in this line of thought due to the apparent lack of universality in application of the BBP to the three basic modern field theories above. This dissertation: (a) analyzes the difficulties by means of algebraic topology, integration theory, and modern differential geometry based on the concepts of principal bundles and Ehresmann connections: (b) extends the BBP to the unified Kaluza-Klein theory; (c) reformulates the inhomogeneous field equations and the BBP in terms of E. Cartan moment of rotation, in the way universal for the three theories and compatible with the original austerity idea; and (d) underlines the important role of the soldering structure on spacetime, and indicates that the future development of the austerity idea would involve the generalized theories.
- Research Organization:
- Texas Univ., Austin (USA)
- OSTI ID:
- 6930249
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ELECTRODYNAMICS
FIELD THEORIES
YANG-MILLS THEORY
DIFFERENTIAL GEOMETRY
DIFFERENTIAL TOPOLOGY
FIELD EQUATIONS
SPACE-TIME
EQUATIONS
GEOMETRY
MATHEMATICS
TOPOLOGY
645400* - High Energy Physics- Field Theory
657003 - Theoretical & Mathematical Physics- Relativity & Gravitation