History state formalism for Dirac’s theory

N. L. Diaz and R. Rossignoli
Phys. Rev. D 99, 045008 – Published 15 February 2019

Abstract

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.

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  • Received 31 May 2018

DOI:https://doi.org/10.1103/PhysRevD.99.045008

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyParticles & Fields

Authors & Affiliations

N. L. Diaz1 and R. Rossignoli1,2

  • 1Departamento de Física-IFLP/CONICET, Universidad Nacional de La Plata, C.C. 67, La Plata (1900), Argentina
  • 2Comisión de Investigaciones Científicas (CIC), La Plata (1900), Argentina

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Vol. 99, Iss. 4 — 15 February 2019

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