History state formalism for Dirac’s theory

• Autores: Díaz, N. L.; Rossignoli, Raúl Dante
• Año de publicación: 2019
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Ciencias Físicas; Dirac´s theory; History states; Quantum entanglement
• Institución: Comisión de Investigaciones Científicas de la Provincia de Buenos Aires

We propose a history state formalism for a Dirac particle. By introducing a reference quantum clock system it is first shown that Dirac’s equation can be derived by enforcing a timeless Wheeler-DeWitt-like equation for a global state. The Hilbert space of the whole system constitutes a unitary representation of the Lorentz group with respect to a properly defined invariant product, and the proper normalization of global states directly ensures standard Dirac’s norm. Moreover, by introducing a second quantum clock, the previous invariant product emerges naturally from a generalized continuity equation. The invariant parameter τ associated with this second clock labels history states for different particles, yielding an observable evolution in the case of a hypothetical superposition of different masses. Analytical expressions for both the space-time density and electron-time entanglement are provided for two particular families of electron states, the former including Pryce localized particles.