Induced representations of tensors and spinors of any rank in the Stueckelberg-Horwitz-Piron theory

Horwitz, L. P.; Zeilig-Hess, Meir

doi:10.1063/1.4928923

Cited by 4 publications

(4 citation statements)

References 31 publications

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“…Since the transformation on the wave function (in ξ or π representation) is independent of π, the expectation value of x μ is covariant. In discussing the two body case later, we remark that this formulation may be applied to any spin (constructed with Clebsch-Gordan products in the spin space [25]).…”

Section: Quantum Theorymentioning

confidence: 99%

“…However, the spin representations we construct are entirely within the local infinitesimal algebra, sufficient to define spin as a local intrinsic structure of the particle (with generators satisfying the Pauli spin algebra). Constructing higher representations from direct product with Clebsch-Gordan coefficients (coordinate independent) can also be done in the same small neighborhood, as can the composition of spins of different particles [25], as we shall do in our discussion of entanglement.…”

Section: Spin Of a Particle In Shpgrmentioning

confidence: 99%

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Spin and entanglement in general relativity

Horwitz

2021

Eur. Phys. J. Plus

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In a previous paper, we have shown how the classical and quantum relativistic dynamics of the Stueckelberg–Horwitz–Piron [SHP] theory can be embedded in general relativity (GR). We briefly review the SHP theory here and, in particular, the formulation of the theory of spin in the framework of relativistic quantum theory. We show here how the quantum theory of relativistic spin can be embedded, using a theorem of Abraham, Marsden and Ratiu and also explicit derivation, into the framework of GR by constructing a local induced representation. The relation to the work of Fock and Ivanenko is also discussed. We show that in a gravitational field there is a highly complex structure for the spin distribution in the support of the wave function. We then discuss entanglement for the spins in a two body system.

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Section: Quantum Theorymentioning

confidence: 99%

Section: Spin Of a Particle In Shpgrmentioning

confidence: 99%

Spin and entanglement in general relativity

Horwitz

2021

Eur. Phys. J. Plus

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“…with L(n) the transformation bringing (1, 0, 0, 0) to n µ . Since the transformatiion on the wave function (in ξ or π representation) is indepedent of π, the expectation value of x µ is covariant.In discussing the two body case later, we remark that this formulation may be applied to any spin (constructed with Clebsch-Gordan products in the spin space [25]).…”

Section: Quantum Theorymentioning

confidence: 99%

“…However, the spin representations we construct are entirely within the local infinitesimal algebra, sufficient to define spin as a local intrinsic structure of the particle (with generators satisfyig the Pauli spin algebra). Constructing higher representations from direct product with Clebsch-Gordan coefficients (coordinate independent) can also be done in the same small neighborhood, as can the composition of spins of different particles [25], as we shall do in our discussion of entanglement.…”

Section: Spin Of a Particle In Shpgrmentioning

confidence: 99%

Spin and Entanglement in General Relativity

Horwitz¹

2020

Preprint

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In a previous paper, we have shown how the classical and quantum relativistic dynamics of the Stueckelberg-Horwitz-Piron [SHP] theory can be embedded in general relativity (GR). We briefly review the SHP theory here and, in particular, the formulation of the theory of spin in the framework of relativistic quantum theory. We show here how the quantum theory of relativistic spin can be embedded, using a theorem of Abraham, Marsden and Ratiu, and also explicit derivation, into the framework of GR by constructing a local induced representation. The relation to the work of Fock and Ivanenko is also discussed. We then discuss entanglement for the spins in a two body system.

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Relativistic entanglement

Horwitz

Arshansky²

2018

Physics Letters A

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The relativistic quantum theory of Stueckelberg, Horwitz and Piron (SHP) describes in a simple way the experiment on interference in time of an electron emitted by femtosecond laser pulses carried out by Lindner et al. In this paper, we show that, in a way similar to our study of the Lindner et al experiment (with some additional discussion of the covarant quantum mechanical description of spin and angular momentum), the experiment proposed by Palacios et al to demonstrate entanglement of a two electron state, where the electrons are separated in time of emission, has a consistent interpretation in terms of the SHP theory. We find, after a simple calculation, results in essential agreement with those of Palacios et al; but with the observed times as values of proper quantum observables. * larry@post.tau.ac.il

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Induced representations of tensors and spinors of any rank in the Stueckelberg-Horwitz-Piron theory

Cited by 4 publications

References 31 publications

Spin and entanglement in general relativity

Spin and entanglement in general relativity

Spin and Entanglement in General Relativity

Relativistic entanglement

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