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This work explores the quantum dynamics of the interaction between scalar(matter) and vectorial (intermediate) particles and studies their thermodynamicequilibrium in the grand-canonical ensemble. The aim of the article is toclarify the connection between the physical degrees of freedom of a theory inboth the quantization process and the description of the thermodynamicequilibrium, in which we see an intimate connection between physical degrees offreedom, Gibbs free energy and the equipartition theorem. We have split thework into two sections. First, we analyze the quantum interaction in thecontext of the generalized scalar Duffin-Kemmer-Petiau quantum electrodynamics(GSDKP) by using the functional formalism. We build the Hamiltonian structurefollowing the Dirac methodology, apply the Faddeev-Senjanovic procedure toobtain the transition amplitude in the generalized Coulomb gauge and, finally,use the Faddeev-Popov-DeWitt method to write the amplitude in covariant form inthe no-mixing gauge. Subsequently, we exclusively use the Matsubara-Fradkin(MF) formalism in order to describe fields in thermodynamical equilibrium. Thecorresponding equations in thermodynamic equilibrium for the scalar, vectorialand ghost sectors are explicitly constructed from which the extraction of thepartition function is straightforward. It is in the construction of thevectorial sector that the emergence and importance of the ghost fields arerevealed: they eliminate the extra non-physical degrees of freedom of thevectorial sector thus maintaining the physical degrees of freedom.

Transition amplitude, partition function and the role of physical degrees of freedom in gauge theories