Position and spin in relativistic quantum mechanics

Zou, L.; Zhang, P. M.; Silenko, Alexander J.

doi:10.1103/physreva.101.032117

Cited by 43 publications

(62 citation statements)

References 144 publications

(385 reference statements)

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“…Note that in the Dirac representation the main part of these operators will not be pure matrix. The usefulness of the Foldy-Wouthuysen transformation is demonstrated recently in [29,30] and in our above mentioned papers as well.…”

Section: Briefly On Application To Symmetry Analysismentioning

confidence: 61%

On the 256-dimensional gamma matrix representation of the Clifford algebra Cl(1,7) and its relation to the Lie algebra SO(1,9)

Simulik¹

2021

Preprint

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The 256-dimensional representations of the Clifford algebras Cℓ R (0,8) and Cℓ R (1,7) in the terms of 8 × 8 Dirac γ matrices are introduced. The corresponding gamma matrix representations of 45-dimensional SO(10) and SO(1,9) algebras, which contain the standard and additional spin operators, are introduced as well. The SO(10), SO(1,9) and corresponding Clifford algebras Cℓ R (0,8), Cℓ R (1,7) are determined as the algebras over the field of real numbers in the space of 8-component spinors. The relationships between the suggested representations of the SO(m,n) and Clifford algebras are investigated. The role of matrix representations of such algebras in the quantum field theory is considered briefly. Our start from the corresponded algebras in the space of standard 4-component Dirac spinors is mentioned. The proposed mathematical objects allow the generalization of our results, obtained earlier for the standard Dirac equation, for the equations of higher spin and, especially, for the equations, describing the particles with spin 3/2. The maximal 84-dimensional pure matrix algebra of invariance of the 8-component Dirac equation in the Foldy-Wouthuysen representation is found. The corresponding symmetry of the Dirac equation is found as well.

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Section: Briefly On Application To Symmetry Analysismentioning

confidence: 61%

On the 256-dimensional gamma matrix representation of the Clifford algebra Cl(1,7) and its relation to the Lie algebra SO(1,9)

Simulik¹

2021

Preprint

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“…As we have mentioned above, various relativistic spin operators have been discussed in the literature, and there is still controversy about which operator can correctly describe the relativistic electron spin. Now let's analyze some conclusions in the literature in detail [23]. We know that for a free Dirac particle, its space-time symmetry can be described by Poincaré group.…”

Section: Basic Equation and Spin Operators For A Free Dirac Particlementioning

confidence: 99%

“…Seven proposals for the relativistic spin operators are summarized in reference [31] and their properties are analyzed mathematically. Although the FW spin operator corresponding to the classical spin vector is considered to be the correct operator to describe the relativistic electron spin in many cases [18,23], the electron in the fully relativistic laser field is usually extremely relativistic and other operators cannot be completely excluded. For this reason, we consider five spin operators which are more likely to describe the real physical spin of a relativistic electron, i.e.…”

Section: Namementioning

confidence: 99%

Identify spin property of relativistic electrons in fully relativistic laser fields

Gan

Wang

et al. 2021

New J. Phys.

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A semiclassical method is developed to study the spin evolution of a relativistic electron in an fully relativistic laser pulse. Different from the previous classical method which is based on the direct generalization of nonrelativistic spin precession equation, we perform first-principle calculations on the mean values of various spin operators with respect to a relativistic electron wavepacket. It is demonstrated, via theoretical derivation and numerical simulation, that although the Foldy-Wouthuysen operator merits the single-particle interpretation, its mean value obviously deviates from the result of the classical method, which sheds light on not only the understanding of relativistic spin itself but also broad related applications. To achieve a direct observation of such effect, a feasible experimental setup utilizing the asymmetric field of a single-cycle laser is proposed. In such geometry, the deviation is evidenced in the total change of spin which can be easily measured after the interaction.

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“…For a quantum-mechanical description of particles in such frames, it is convenient to apply the Foldy-Wouthuysen (FW) representation providing for the Schrödinger picture of relativistic quantum mechanics (see Refs. [32,33] and references therein). The relativistic FW Hamiltonian describing a spin-1/2 particle in the frame uniformly rotating with the angular velocity ω has the form [34]…”

mentioning

confidence: 99%

“…The corresponding relativistic FW Hamiltonian has been obtained in Refs. [33,54,55]. It contains spinindependent and spin-dependent terms and is the same for untwisted and twisted spin-1/2 particles.…”

mentioning

confidence: 99%

Twisted particles in heavy-ion collisions

Silenko¹,

Zhang²,

Zou³

2021

Proceedings of 40th International Conference on High Energy Physics — PoS(ICHEP2020)

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The importance of twisted (vortex) particles in heavy-ion collisions is analyzed. Free twisted particles can possess giant intrinsic orbital angular momenta. Twisted particles are spatially localized and can be rather ubiquitous in laboratories and nature. Twisted photons have nonzero effective masses. Charged twisted particles can be recognized by their dynamics, magnetic moments, and specific effects in external fields.

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Position and spin in relativistic quantum mechanics

Cited by 43 publications

References 144 publications

On the 256-dimensional gamma matrix representation of the Clifford algebra Cl(1,7) and its relation to the Lie algebra SO(1,9)

On the 256-dimensional gamma matrix representation of the Clifford algebra Cl(1,7) and its relation to the Lie algebra SO(1,9)

Identify spin property of relativistic electrons in fully relativistic laser fields

Twisted particles in heavy-ion collisions

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