Quasiprobabilities and explicitly covariant relativistic quantum theory

The concepts and formalism of quasiprobabilities in the space of paths are extended to the relativistic domain. The definition of a relativistic wave function, needed in the construction of the quasiprobability functional, is discussed extensively, together with the formulation and the physical interpretation of an explicitly covariant quantum theory. The Wigner and the Margenau-Hill relativistic phase-space distribution functions are then obtained according to the standard procedures of the formalism.