Mathematics
Scientific paper
Dec 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985phdt........18s&link_type=abstract
Ph.D. Thesis Maryland Univ., College Park.
Mathematics
2
Broken Symmetry, Manifolds (Mathematics), Quantum Mechanics, Anisotropy, Curvature, Einstein Equations, Scalars, Topology
Scientific paper
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 of lambda phi to the 4th power field with arbitrary coupling Xi is computed by zeta function regularization. We find that for massless minimal coupled scalar field, first order phase transition 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 M4 x Tn and M4 x (taub) to the 3rd power spaces are obtained. The stability criterions for the static solutions of the self-consistent Einstein equations are derived. We find the stable solutions of the M4 x SN 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.
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