Finite Temperature and Density Effects in Higher Dimensions with and without Compactifications

Expressions for the thermodynamic potential of a Dirac fermion gas are represented at finite temperature with the chemical potential in an ultrastatic space $R^d\times S^N$. The high- and low- temperature expansions for the thermodynamic potential are obtained and, in particular, strongly degenerate fermi gas is investigated. For the Candelas-Weinberg model, sufficiently high "charge" density prevents the compactification of the extra space.

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