Matrix relativity and gauge fields
In this thesis the author assumes the validity of Einstein's Relativity for the description of the gravitational phenomena and address the problem of unification of the latter with gauge theories of the Yang-Mills type. For this purpose the author has developed a formalism called Matrix Relativity, in which the usual metric tensor and affine connection are provided with internal degrees of freedom. This amounts to considering these objects as matrix-valued fields defined on a four dimensional space-time. Having defined and constructed the basic elements of the theory in Chapter II, the authors first observes that the formalism allows the establishment of a larger group of covariance for the matrix curvature tensor by means of a generalized gauge transformation, that includes general coordinate and N-dimensional unitary transformations as special cases. However, use of this covariance for the construction of invariant lagrangians seems to yield physically unacceptable models. The difficulty associated with the non-abelian nature of the field variables is circumvented in the model discussed in Chapter III, in which use is made of the Einstein ansatz. We also study an alternative model in which the matrix affine connection is required to satisfy the quasi-metric condition.
- Research Organization:
- Rochester Univ., NY (USA)
- OSTI ID:
- 5135488
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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