Paper detail

Quantum Processes and Energy-Momentum Flow

In this paper we focus on energy flows in simple quantum systems. This is achieved by concentrating on the quantum Hamilton-Jacobi equation. We show how this equation appears in the standard quantum formalism in essentially three different but related ways, from the standard Schrödingier equation, from Lagrangian field theory and from the von Neumann-Moyal algebra. This equation allows us to track the energy flow using the energy-momentum tensor, the components of which are related to weak values of the four-momentum operator. This opens up a new way to explore these components empirically. The algebraic approach enables us to discuss the physical significance of the underlying non-commutative symplectic geometry, raising questions as to the structure of particles in quantum systems.