Uniqueness of conserved currents in quantum mechanics

Abstract

It is proved by a functional method that the conventional expression for the Dirac current is the only conserved 4-vector implied by the Dirac equation that is a function of just the quantum state. The demonstration is extended to derive the unique conserved currents implied by the coupled Maxwell-Dirac equations and the Klein-Gordon equation. The uniqueness of the usual Pauli and Schrodinger currents follows by regarding these as the non-relativistic limits of the Dirac and Klein-Gordon currents, respectively. The existence and properties of further conserved vectors that are not functions of just the state is examined.

22 pages

Cited by in corpus (22)

• Implications of Lorentz covariance for the guidance equation in two-slit quantum interference
• Computing the wavefunction from trajectories: particle and wave pictures in quantum mechanics and their relation
• Arrival Time Distributions of Spin-1/2 Particles
• Quantum Mechanics of Klein-Gordon Fields I: Hilbert Space, Localized States, and Chiral Symmetry
• Non-relativistic limits of Maxwell's equations
• Exotic Bohmian arrival times of spin-1/2 particles I-An analytical treatment
• Quantum non-equilibrium and relaxation to equilibrium for a class of de Broglie-Bohm-type theories
• Hydrodynamic construction of the electromagnetic field
• On the uniqueness of paths for spin-0 and spin-1 quantum mechanics
• Weakly nonlocal fluid mechanics - the Schrodinger equation
• The Pauli and $\text{Leˊvy-Leblond}$ Equations, and the Spin Current Density
• On simulation of local fluxes in molecular junctions
• Quantum time of flight distribution for cold trapped atoms
• Observability of the arrival time distribution using spin-rotator as a quantum clock
• Quantitative probing of quantum-classical transition for the arrival time distribution
• Effect of quantum statistics on the gravitational weak equivalence principle
• Trajectory-state theory of the Klein-Gordon field
• Conserved Current Densities, Localization Probabilities, and a New Global Gauge Symmetry of Klein-Gordon Fields
• Trajectory construction of Dirac evolution
• A survey on uncertainty relations and quantum measurements
• Unification of the wave and guidance equations for spin 1/2
• Quantum interference in the time-of-flight distribution