Quantum effects in non-maximally symmetric spaces
Non-Maximally symmetric spaces provide a more general background to explore the relation between the geometry of the manifold and the quantum fields defined in the manifold than those with maximally symmetric spaces. A static Taub universe is used to study the effect of curvature anisotropy on the spontaneous symmetry breaking of a self-interacting scalar field. The one-loop effective potential on a lambdaphi/sup 4/ field with arbitrary coupling xi is computed by zeta function regularization. For massless minimal coupled scalar fields, first order phase transitions can occur. Keeping the shape invariant but decreasing the curvature radius of the universe induces symmetry breaking. If the curvature radius is held constant, increasing deformation can restore the symmetry. Studies on the higher-dimensional Kaluza-Klein theories are also focused on the deformation effect. Using the dimensional regularization, the effective potential of the free scalar fields in M/sup 4/ x T/sup N/ and M/sup 4/ x (Taub)/sup 3/ spaces are obtained. The stability criterions for the static solutions of the self-consistent Einstein equations are derived. Stable solutions of the M/sup 4/ x S/sup N/ topology do not exist. With the Taub space as the internal space, the gauge coupling constants of SU(2), and U(1) can be determined geometrically. The weak angle is therefore predicted by geometry in this model.
- Research Organization:
- Maryland Univ., College Park (USA)
- OSTI ID:
- 7103913
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MATHEMATICAL MANIFOLDS
MATHEMATICAL SPACE
SYMMETRY
QUANTUM FIELD THEORY
UNIVERSE
SYMMETRY BREAKING
EINSTEIN FIELD EQUATIONS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
SPACE
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