Second-Quantization Process for Particles with Any Spin and with Internal Symmetry

Nelson, T. J.; Good, R. H.

doi:10.1103/revmodphys.40.508

Cited by 29 publications

(7 citation statements)

References 21 publications

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“…The Clifford-Dirac anticommutation relations for the matrices (93) are similar. The γ matrices (93), (94) generate the 29 dimensional representation of the proper extended real Clifford-Dirac algebra SO (8), which was introduced in [24][25][26][27][28]. Both the fundamental representation…”

Section: Doubletmentioning

confidence: 99%

“…The additional possibilities, which are open by the additional 29 orts of algebra SO (8) in comparison with 16 orts of the standard Clifford-Dirac algebra, are principal in description of the Bose states in the framework of the Dirac theory [24][25][26][27][28]. The algebra SO(8) includes two independent SU(2) subalgebras (γ 2 γ 3 , γ 3 γ 1 , γ 1 γ 2 ) and (γ 5 γ 6 , γ 6 γ 4 , γ 4 γ 5 ), when the standard Clifford-Dirac algebra includes only one given by the elements (γ 2 γ 3 , γ 3 γ 1 , γ 1 γ 2 ).…”

Section: Doubletmentioning

confidence: 99%

“…Different approaches to the description of the particles of an arbitrary spin can be found in [4][5][6][7][8][9][10][11][12]. The allusion on the RCQM and the first steps are given in [13].…”

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confidence: 99%

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Covariant local field theory equations following from the relativistic canonical quantum mechanics of arbitrary spin

Simulik¹

2014

Preprint

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The new relativistic equations of motion for the particles with spin s=1, s=3/2, s=2 and nonzero mass have been introduced. The description of the relativistic canonical quantum mechanics of the arbitrary mass and spin has been given. The link between the relativistic canonical quantum mechanics of the arbitrary spin and the covariant local field theory has been found. The manifestly covariant field equations that follow from the quantum mechanical equations, have been considered. The covariant local field theory equations for spin s=(1,1) particle-antiparticle doublet, spin s=(1,0,1,0) particle-antiparticle multiplet, spin s=(3/2,3/2) particle-antiparticle doublet, spin s=(2,2) particle-antiparticle doublet, spin s=(2,0,2,0) particle-antiparticle multiplet and spin s=(2,1,2,1) particle-antiparticle multiplet have been introduced. The Maxwell-like equations for the boson with spin s=1 and m > 0 have been introduced as well.

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Section: Doubletmentioning

confidence: 99%

Section: Doubletmentioning

confidence: 99%

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Covariant local field theory equations following from the relativistic canonical quantum mechanics of arbitrary spin

Simulik¹

2014

Preprint

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“…Different approaches to the description of the field theory of an arbitrary spin can be found in [7,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Here and in [1][2][3] only the approach started in [7] is the basis for further application.…”

mentioning

confidence: 99%

“…Therefore, the partial differential equations for arbitrary spin found in [1][2][3] are without redundant components. It is the advantage of equations from [1][2][3] in comparison with equations considered in [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56].…”

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confidence: 99%

On the Relativistic Canonical Quantum Mechanics and Field Theory of Arbitrary Spin

Simulik¹

2017

ujpa

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The new relativistic equations of motion for the particles with arbitrary spin and nonzero mass, suggested by author in years 2014-2016, are under consideration. The complete version of brief paper in J. Phys: Conf. Ser., 670 (2016) 012047(1-16) is given. The axiomatic level description of the relativistic canonical quantum mechanics of an arbitrary mass and spin has been given. The 64-dimensional Cl R (0,6) algebra in terms of Dirac gamma matrices has been suggested. The interpretation of the 28-dimensional gamma matrix representation of SO(8) algebra over the field of real numbers is given. The link between the relativistic canonical quantum mechanics of the arbitrary spin and the covariant local field theory in the form of extended Foldy-Wouthuysen transformation has been found. Different methods of the Dirac equation derivation have been reviewed. The manifestly covariant field equation for an arbitrary spin, that follows from the corresponding equation of relativistic canonical quantum mechanics, has been considered. The found equations are without redundant components. The partial examples for spin s=3/2 and s=2 are presented. The covariant local field theory equations for spin s = (3/2,3/2) particle-antiparticle doublet and spin s = (2,2) particle-antiparticle doublet have been introduced. The Maxwell and slightly generalized Maxwell-like equations containing mass member have been considered as well.

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Bose quantization of a new spin-1/2 equation

Guertin

1975

Int J Theor Phys

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We second quantize a relativistic Schr6dinger equation involving a Hamiltonian H that describes free spin-½ particles and that depends on a parameter G. We require a positive definite metric and a positive definite energy in the Fock space in which the field qJ (x, t) and its adjoint operate. If G = ±i, one obtains the usual second-quantized Dirac theory, but for real values of G one has Bose statistics. Whereas the anticommutator [~(x, t), ~*(x', t')]. vanishes for a Dirac field when the interval between (x, t) and (x', t') lies outside the light cone, when G is real the commutator [¢(x, t), ~ *(x', t')]_ vanishes for such points. t. IntroductionIn an earlier paper (Guertin, 1975b), we studied a Schr6dinger equation involving a Hamiltonian that is a second-order differential operator, describes free spin-½ particles with both energy signs and a definite mass, and depends on a parameter G. By setting G = -+i one obtains the usual Dirac Hamiltonian, but for real values of G the one-particle theory possesses an indefinite metric; thus, negative energy states have a negative normalization, as in the SakataTaketani spin-0 and spin-1 Hamiltonian theories (Sakata & Taketani, 1940;Heitler, 1943) and their arbitrary spin generalizations (Guertin, 1974(Guertin, , 1975a. In this paper we second-quantize the theory using Bose statistics for real values of G and find that, for such values of G, the commutator of the field and its adjoint vanishes when the interval between their space-time arguments is spacelike.

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Second-Quantization Process for Particles with Any Spin and with Internal Symmetry

Cited by 29 publications

References 21 publications

Covariant local field theory equations following from the relativistic canonical quantum mechanics of arbitrary spin

Covariant local field theory equations following from the relativistic canonical quantum mechanics of arbitrary spin

On the Relativistic Canonical Quantum Mechanics and Field Theory of Arbitrary Spin

Bose quantization of a new spin-1/2 equation

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