Articulo
History state formalism for Dirac’s theory
Registro en:
issn:2470-0010
issn:2470-0029
Autor
Díaz, Nahuel Luciano
Rossignoli, Raúl Dante
Institución
Resumen
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. Instituto de Física La Plata Comisión de Investigaciones Científicas de la provincia de Buenos Aires