History state formalism for Dirac’s theory

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...

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Autores principales: Díaz, Nahuel Luciano, Rossignoli, Raúl Dante
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2019
Materias:
Física
Quantum entanglement
Physics
Lorentz group
Invariant (physics)
Superposition principle
Unitary representation
Observable
Quantum clock
Mathematical physics
Hilbert space
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/124980
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-124980
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Quantum entanglement
Physics
Lorentz group
Invariant (physics)
Superposition principle
Unitary representation
Observable
Quantum clock
Mathematical physics
Hilbert space
spellingShingle Física
Quantum entanglement
Physics
Lorentz group
Invariant (physics)
Superposition principle
Unitary representation
Observable
Quantum clock
Mathematical physics
Hilbert space
Díaz, Nahuel Luciano
Rossignoli, Raúl Dante
History state formalism for Dirac’s theory
topic_facet Física
Quantum entanglement
Physics
Lorentz group
Invariant (physics)
Superposition principle
Unitary representation
Observable
Quantum clock
Mathematical physics
Hilbert space
description 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.
format Articulo
Preprint
author Díaz, Nahuel Luciano
Rossignoli, Raúl Dante
author_facet Díaz, Nahuel Luciano
Rossignoli, Raúl Dante
author_sort Díaz, Nahuel Luciano
title History state formalism for Dirac’s theory
title_short History state formalism for Dirac’s theory
title_full History state formalism for Dirac’s theory
title_fullStr History state formalism for Dirac’s theory
title_full_unstemmed History state formalism for Dirac’s theory
title_sort history state formalism for dirac’s theory
publishDate 2019
url http://sedici.unlp.edu.ar/handle/10915/124980
work_keys_str_mv AT diaznahuelluciano historystateformalismfordiracstheory
AT rossignolirauldante historystateformalismfordiracstheory
bdutipo_str Repositorios
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