Bose-Einstein condensation in many-particle gauge theories and external charge

Summary  The realization of the charged Bose-Einstein condensation in gauge theories with finite particle density is investigated. Examples are found for a situation in which two charged Bose-Einstein condensates coexist in equilibrium in systems described by Abelian gauge theories. Also Abelian and non-Abelian systems are constructed for which a charged Bose-Einstein condensate is balanced by the charge of a fermionic subsystem. A limiting transition to infinitely heavy fermions with infinite chemical potential is pointed out, which turns the fermionic subsystem into an external charge in an Abelian theory. On the contrary, the non-Abelian gauge theory with external charge cannot be obtained by the same dynamical limiting process since it requires a special quantization scheme. It is realized for the Yang-Mills-Higgs model with a constant external charge. Eigenfrequencies of the system are found, which include an additional quantum degree of freedom induced by the external charge. The contribution of the eigenfrequencies to the thermodynamical potential is found.