An effective relativistic continuum massive Proca Lagrangian action is used to account for the Lorentzvector condensation effects on the equation of state of the strongly interacting fermions system.The interior quantumfluctuation effects are incorporated as an external field approximation indirectly through a fictive generalized ThomsonProblem counterterm background.The general analytical formulas for the d-dimensional thermodynamics are given nearthe unitary limit region,In the non-relativistic limit for d=3,the universal dimensionless coeff...