Physics
Scientific paper
Mar 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982phdt........31g&link_type=abstract
Thesis (PH.D.)--NORTH CAROLINA STATE UNIVERSITY, 1982.Source: Dissertation Abstracts International, Volume: 43-03, Section: B, p
Physics
3
Scientific paper
This dissertation provides an investigation of certain fundamental invariance and symmetry properties of field theories and their structures at the classical level. Our results provide insight into the physical roles of invariance properties and symmetry demands in the context of various field theoretical models. We stress the role of the conformal and projective properties of the space -time structure. However, more generally, we are concerned with transformations which leave the trace of the Ricci tensor invariant. These objectives are approached by first considering particular types of symmetry conditions that can be characterized by point mappings on a given space-time. After considering the symmetry conditions, invariance properties are examined as free transformations in the context of particular physical models. Symmetry properties which are members of the Family of Contracted Ricci Collineations (FCRC) are considered. Several theorems are given concerning FCRC symmetry properties. While the major part of the investigation is restricted to Einstein's theory, the extension of these results to ECSK theory is discussed. A symmetry property which cannot, in general, be characterized in terms of Lie deformations is the existence of a Killing tensor. The form of all metric tensors which admit Killing tensors with a Segre characteristic {1(111) } which have non-constant eigenvalues is found. The role of conformal invariance in various field theoretical models is examined. Particular attention is given to conformal invariance in theories which have a variable "gravitational constant". While most previous investigations in this area have been restricted to considering symmetric connections, we are chiefly concerned with space -times with a general metric connection. A new type of conformal invariance, which couples conformal transformations on the metric tensor to projective transformations on the torsion tensor and preserves metricity, is discussed. We show that many of the conclusions previously obtained concerning the relationship between conformal invariance and variable "gravitational constant" theories are not valid in these more general space-times. The significance of a special type of projective invariance is investigated in the context of the metric affine theory and their extensions. This particular type of invariance property has been interpreted by Davis and later Baker as being associated with baryon number conservation.
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