Fiber-bundle approach to unified field theory
It is shown that the Einstein, Maxwell and Dirac equations are special cases of a fiber-bundle approach to unified field theory when based on the gauge transformations of the group SU(4/N). This group is rearranged into a modified SU(2,2/N) group which directly contains Dirac generators in the supersymmetry or Fermi part, and is shown to contain SU(2,2)xSU(N)xU(1) in its commuting or Bose part. The action is constructed based on the scalar curvature of the fiber-bundle and is invariant, under space-time coordinate changes and gauge transformations, when integrated over spacetime and group space. A finite change in the gauge potentials allows the lower spin O and spin 1/2 components to enter. Minor changes in the relationship between constants in the theory allows different chiral contributions to occur in the Dirac equation, favoring left-or-right-handed interactions. No restrictions are given which determine this relationship, but a choice is made to demonstrate the presence of the Dirac equation. The scaling requirements onthe electromagnetic and Dirac actions fixes the size of the contribution from the Weyl action for gravity. It is found to be approx. 10/sup 65/ weaker than Einstein's gravitational action and therefore this approach avoids the problems assiciated with the R + R/sup 2/ lagrangian. Finally, it is mentioned how the group SU(4/3) might be used to construct an action which would contain the Weinberg-Salam model, to lowest order, and naturally introduce all appropriate fields.
- OSTI ID:
- 5976804
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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UNIFIED GAUGE MODELS
DIRAC EQUATION
EINSTEIN FIELD EQUATIONS
FIBERS
MATHEMATICAL MODELS
MAXWELL EQUATIONS
SU GROUPS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD EQUATIONS
LIE GROUPS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
SYMMETRY GROUPS
WAVE EQUATIONS
645400* - High Energy Physics- Field Theory