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

Simulik, V. M.

doi:10.13189/ujpa.2017.110602

Cited by 2 publications

(2 citation statements)

References 128 publications

(470 reference statements)

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“…As well recently, we have the link between the relativistic canonical quantum mechanics of arbitrary spin and the covariant local field theory by V.M. Simulik (2017) [9] (where the found equations are without redundant components).…”

Section: Introductionmentioning

confidence: 99%

On the Fisk–Tait equation for spin-3/2 fermions interacting with an external magnetic field in noncommutative space-time

Haouam¹

2020

J. Phys. Stud.

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The Fisk-Tait equation in interaction with an external magnetic field in noncommutative spacetime is investigated, consequently, we studied the continuity equation in both commutative and noncommutative space-time; there we examined the influence of the space-time noncommutativity on the current density quadri-vector. And we also find that the total charge obtained from the probability density still indefinite even when space does not commute. Furthermore we found the spin current density in the two different spin directions. We also investigated the linking between the fermions and the bosons in the Fock space using the Holstein-Primakoff transformation.Over the years the particle equations for an arbitrary spin was considered the subject for careful investigations, that's why today we are interested in the relativistic equations that describe the motion of spin-3/2 particles. Such as the relativistic Rarita-Schwinger equation (1940) [1], the Fisk-Tait equation (1973) [2], Hurley's field equation [3], Bhabha-Gupta equation (Bhabha, Gupta 1952, 1954, 1974, the approach for arbitrary spin equation by V. Bargman, E.P. Wigner (1948) [6]. Also the Heisenberg equations of motion for the spin-3/2 field (1977) [7], in which, it is shown for dynamical systems with constraints depending upon external fields, the Lagrange and Heisenberg equations of motion are the same for the quantized charged spin-3/2 field in the presence of a minimal external electromagnetic interaction. The Rarita-Schwinger spin-3/2 equation in the weak-field limit is obtained to satisfy the Heisenberg equations of motion. This is similar to the case of spin-3/2 field minimally coupled with an external electromagnetic field by Mainland and Sudarshan (1973) [8].As well recently, we have the link between the relativistic canonical quantum mechanics of arbitrary spin and the covariant local field theory by V.M. Simulik (2017) [9] (where the found equations are without redundant components). Where it has been confirmed that, the synthesis of the relativistic canonical quantum mechanics of the spins-3/2 particle and antiparticle doublet is completely similar to the synthesis of the Dirac equation from the relativistic canonical quantum mechanics of the spin-1/2 particle-antiparticle doublet. On the basis of the investigation of solutions and transformation properties with respect to the Poincare group the obtained new 8-component equation is suggested to be well defined for the description of spin s=3/2 fermions. Despite the Rarita-Schwinger equation which has 16 components and needs the additional condition.But the equation for a particle of spin-3/2 originally was given by Fierz and Pauli (I939) in spinor form [10]. Knowing that the Klein-Gordon, Dirac, and Proca equations provide a relativistic description of the particles that have the lowest spins cases (S=0, 1/2, 1 respectively).For instance, the Rarita-Schwinger equation was formulated for the first time by William Rarita and Julian Schwinger, it was the most famous equation that describes the m...

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Section: Introductionmentioning

confidence: 99%

On the Fisk–Tait equation for spin-3/2 fermions interacting with an external magnetic field in noncommutative space-time

Haouam¹

2020

J. Phys. Stud.

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“…Today, the Pauli-Fierz [4], Bhabha [5], and Bargmann-Wigner [6] equations and their contemporary modifications (see, e. g. [7]) are most often considered. A more detailed review can be found in [8]. Here, in [1] and [2], only the approach started in [9] and [10] is the basis for the further application.…”

Section: Introductionmentioning

confidence: 99%

Relativistic Equations for Arbitrary Spin, Especially for the Spin s = 2

Simulik

2019

Ukr. J. Phys.

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The further approbation of the equation for the particles of arbitrary spin introduced recently in our papers is under consideration. The comparison with the known equations suggested by Bhabha, Pauli–Fierz, Bargmann–Wigner, Rarita–Schwinger (for spin s =3/2) and other authors is discussed. The advantages of the new equations are considered briefly. The advantage of the new equation is the absence of redundant components. The important partial case of spin s =2 is considered in details. The 10-component Dirac-like wave equation for the spin s =(2,2) particle-antiparticle doublet is suggested. The Poincar´e invariance is proved. The three-level consideration (relativistic canonical quantum mechanics, canonical Foldy–Wouthuysen-type field theory, and locally covariant field theory) is presented. The procedure of our synthesis of arbitrary spin covariant particle equations is demonstrated on the example of spin s =(2,2) doublet.

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

Cited by 2 publications

References 128 publications

On the Fisk–Tait equation for spin-3/2 fermions interacting with an external magnetic field in noncommutative space-time

On the Fisk–Tait equation for spin-3/2 fermions interacting with an external magnetic field in noncommutative space-time

Relativistic Equations for Arbitrary Spin, Especially for the Spin s = 2

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