Spacetime Quantum Actions

TL;DR

This paper introduces a novel quantum framework extending Fock space to include time, enabling a unified description of quantum histories, correlations, and dynamics with implications for relativistic theories and path integrals.

Contribution

It presents a new formulation of quantum mechanics using an extended Fock space with tensor products over time, generalizing classical actions and unifying various quantum theories.

Findings

Recovering conventional quantum mechanics predictions

Establishing extended unitary equivalence between theories

Providing rigorous meaning to quantum correlations across time

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.