Generalization of the Boguliubov Method Applied to Mixtures of Bose-Einstein Particles

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Abstract
The method developed by Boguliubov for an imperfect Bose-Einstein gas is generalized in order to permit examination of a mixture of an arbitrary number of different species of bosons. The generalized method involves diagonalization of a matrix which has a Hermitian-like property by a unitary-like transformation in a space with an indefinite metric. When a neutral mixture of two types of charge bosons is examined, it is found that two types of elementary excitations exist; one having the energy-momentum dispersion relation associated with plasma oscillations at low momenta and another having the energy-momentum relationship characteristic of a free particle with a modified mass at very low and high momenta. Further investigation shows that the plasma-type excitation consists of an oscillation in charge density while the free-particle-like excitation consists of an oscillation in mass density.