On the Properties of a Bose gas in Spaces with Dimensions n = 1, 2, 4 Within the Framework of the General Theory of a Space with n Dimensions

Abstract

An ideal Bose gas is considered within the framework of the general case of a space with n dimensions with a different technique for obtaining the well-known result of the absence of its condensed phase in spaces of lower dimensions n = 1, 2. It is also shown that, as in the case n = 3, at the degeneracy temperature there is a jump in the temperature derivative of the heat capacity in spaces with n > 3, and the curve of the heat capacity itself has a maximum with a break at this temperature with a specific character for n = 4 that is different than for the other values. Taking interaction effects into account, this leads to the appearance of a second-order phase transition for all n = 3… with a jump-like increase in the heat capacity at the transition from one symmetric phase of matter to another, less symmetric phase, which can be of interest in the context of models of the early Multi-Universe. Possible applications of the results of this paper in the realm of cosmology are discussed; in particular, a possible variant of the solution of the problem of dark matter is proposed.