Finite temperature and vacuum effects in higher dimensions

Mathematics

Scientific paper

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Free Energy, Quantum Theory, Space-Time Functions, Thermal Stability, Unified Field Theory, Vacuum Effects, Zero Point Energy, Manifolds (Mathematics), Scalars, Spheres, Thermodynamics, Topology, Toruses

Scientific paper

Some general formulae, including high and low temperature forms, are
developed for the free energy of a scalar field on the product manifold
R x (R to the n power) x (M sub d). The role and effect of zero modes is
considered and specific calculations are made for the cases when the
internal space, M sub d, is a torus and a sphere.

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