Spin and localization of relativistic fermions and uncertainty relations

The problem of the position and spin in relativistic quantum mechanics is analyzed in detail. It is definitively shown that the position and spin operators in the Foldy-Wouthuysen representation (but not in the Dirac one) are quantum-mechanical counterparts of the classical position and spin variables. The probabilistic interpretation is valid only for Foldy-Wouthuysen wave functions. The relativistic spin operators are discussed. The spin-orbit interaction does not exist for a free particle if the conventional operators of the orbital angular momentum and the rest-frame spin are used.Alternative definitions of the orbital angular momentum and the spin are based on noncommutative geometry, do not satisfy standard commutation relations, and can allow the spin-orbit interaction. * zoulp@impcas.ac.cn †

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“…The use of Eqs. (36), (59), and (62) shows that s ′ = s. This result has been first obtained by Ryder [56] (see also Ref. [59]).…”

Section: Relativistic Operators Of the Position And Spinsupporting

confidence: 71%

Position and spin in relativistic quantum mechanics

2020

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“…We expect that in the Dirac theory can be constructed the relativistic generalization of the spin operator (84). The question on the definition of a conventional spin operator has been raised a long time ago [75,76] and is under discussion up to date [77][78][79]. Many people noticed that in the Dirac theory it is possible to construct other operators that obey reasonable equations; see [16,80].…”

Section: (3) Velocity Of An Electron Since the Velocity Operatormentioning

confidence: 99%

“…As the speed of the particle closes to the critical velocity, the longitudinal acceleration diverges due to the first term in (79). In resume, assuming that MPTD particle sees the original geometry 휇] , we have a theory with unsatisfactory behavior in the ultrarelativistic limit.…”

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Дериглазов

Ramírez

2017

Advances in Mathematical Physics

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We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: (A) one-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic Zitterbewegung; (B) spin-induced noncommutativity and the problem of covariant formalism; (C) three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; (D) paradoxical behavior of the Mathisson-PapapetrouTulczyjew-Dixon equations of a rotating body in ultrarelativistic limit, and equations with improved behavior.

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“…(12) the previous pseudoeuclidean inner product becomes isomorphic to two euclidean products. This is a consequence of the following relations [22]:ū…”

Section: B Free Dirac's Particlementioning

confidence: 95%

History state formalism for Dirac’s theory

Díaz

Rossignoli

2019

Phys. Rev. D

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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 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 an hypothetical superposition of different masses. Analytical expressions for both space-time density and electrontime entanglement are provided for two particular families of electron's states, the former including Pryce localized particles.

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Spin and localization of relativistic fermions and uncertainty relations

Cited by 35 publications

References 74 publications

Position and spin in relativistic quantum mechanics

Position and spin in relativistic quantum mechanics

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

History state formalism for Dirac’s theory

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