Bhabha relativistic wave equations

Loide, R.-K.; Ots, I.; Saar, R.

doi:10.1088/0305-4470/30/11/027

Cited by 20 publications

(30 citation statements)

References 30 publications

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“…where the matricesΓ A 2N are given in (38), (52). The situation here is similar to the FW representation.…”

Section: On the Relativistic Canonical Quantum Mechanics And Field Thmentioning

confidence: 99%

“…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.…”

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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%

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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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“…where the matricesΓ A 2N are given in (38), (52). The situation here is similar to the FW representation.…”

Section: On the Relativistic Canonical Quantum Mechanics And Field Thmentioning

confidence: 99%

mentioning

confidence: 99%

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

Simulik¹

2017

ujpa

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“…Analogous considerations are applicable in the superfield case [5,6,7]. To consider irreducible Lorentz superfields ψ i (x, θ), ψ j (x, θ), .…”

Section: Superfield Equations Of Motion Superspin Projection Operatorsmentioning

confidence: 99%

Supersymmetry: superfield equations of motion

Loide

Suurvarik

2014

J. Phys.: Conf. Ser.

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Abstract. Supersymmetry and superfields are considered in connection with Poincaré superalgebras. A formalism of projection operators for deriving wave equations for ordinary fields and superfields is developed. Superfield equations of motion in the case of massive and massless fields are presented together with an application in linear supergravity.1. Supersymmetry, superfields, Poincaré superalgebra Supersymmetry has been known more than few decades, but it is still alive despite the absence of experimental verification. Supersymmetry offers several relevant theoretical solutions for modern physics. Supersymmetry (Bose-Fermi symmetry)Let us consider a general N = 1 superfieldwhere θ α is a four-component anticommuting Majorana spinor and i is a Lorentz index. Now we introduce the most general Poincaré superalgebra [1]. The generators of the Poincaré group P µ and M µν , and n supergenerators S α (α = 1, 2, . . . , n) satisfy the following relations:where η µν = diag(+ ---). The simple N = 1 supersymmetry algebra is related to the bispinor representation of the Lorentz group. We have four bispinor generators S α , B µν = 1 2 σ µν and A µ = γ µ C. The Nextended Poincaré superalgebra is related to the direct sum of N bispinor representations. New possibilities [2]• In the most general case the matrices A µ are related to the β-matrices of an invariant first order wave equation

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“…2 Interest in the Bhabha equation has been increased recently 3 by the fact that all relativistic equations for particles with spin sϾ1/2 ͑Duffin-Kemmer, Fierz-Pauli, Bargmann-Wigner equations͒, are particular cases of the Bhabha equation ͑sometimes with additional conditions͒. Recently, a simpler way was proposed 4 by a research group including the present authors, to ''derive'' the Bhabha equation in a Lorentz-covariant way, and to study its properties using the canonical chain of orthogonal groups O(5)ʛO (4)ʛO (3)ʛO (2). The equation is written in terms of the generators ⌳ 5 (ϭ1,2,3,4) of the group O(5) as 4 ͑ 2ic⌳ i5 p i ϩ2c⌳ 45 p 0 ϩnmc 2 ͒ϭ0, ͑1͒…”

Section: Introductionmentioning

confidence: 99%

Spin-mass content of the Bhabha particle and the group chain SU(4)⊃Sp(4)⊃SU(2)×U(1)

Smirnov

Sharma

1999

Journal of Mathematical Physics

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The relativistic particles described by the Bhabha equation ͑Bhabha particles͒ can possess several values of masses (M ϭn/2) and spins sрn/2. In order to find the spin-mass content of such particles corresponding to the general irrep ͗n 1 n 2 ͘ of the group Sp(4)ϳO(5) which is the symmetry group of the Bhabha equation, the noncanonical chain of groups Sp(4)ʛSU s (2)ϫU (1) is considered. In this paper, we construct the basis of the irrep ͗n 1 n 2 ͘ in a boson realization form using the method of elementary permissible diagrams. This is achieved by the introduction of special ''symplectic'' bosons. The maximum and minimum values of spin s are established for each value of . The multiplicity of degenerate pairs (s,t) can be easily calculated with the help of the generating function obtained in this paper.

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Bhabha relativistic wave equations

Cited by 20 publications

References 30 publications

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

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

Supersymmetry: superfield equations of motion

Spin-mass content of the Bhabha particle and the group chain SU(4)⊃Sp(4)⊃SU(2)×U(1)

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