Space-time quantum actions

Abstract

We propose a formulation of quantum mechanics in an extended Fock space in which a tensor product structure is applied to time. Subspaces of histories consistent with the dynamics of a particular theory are defined by a direct quantum generalization of the corresponding classical action. The diagonalization of such quantum actions enables us to recover the predictions of conventional quantum mechanics and reveals an extended unitary equivalence between all physical theories. Quantum correlations and coherent effects across time and between distinct theories acquire a rigorous meaning, which is encoded in the rich temporal structure of physical states. Connections with modern relativistic schemes and the path integral formulation also emerge.