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تسجيل مستخدم جديدHistory state formalism for Diracs theory
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We propose a history state formalism for a Dirac particle. By introducing a reference quantum clock system it is first shown that Diracs 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 Diracs norm. Moreover, by introducing a second quantum clock, the previous invariant product emerges naturally from a generalized continuity equation. The invariant parameter $tau$ associated with this second clock labels history states for different particles, yielding an observable evolution in the case of an hypothetical superposition of different masses. Analytical expressions for both space-time density and electron-time entanglement are provided for two particular families of electrons states, the former including Pryce localized particles.
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