The algebra of meson matrices

Kemmer, N.; Wilson, A. H.

doi:10.1017/s0305004100017874

Cited by 63 publications

(58 citation statements)

References 6 publications

(5 reference statements)

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“…with 5 × 5 and 10 × 10 matrices β µ , respectively, which fulfill the following commutation relations [26][27][28][29]:…”

Section: The Duffin-kemmer-petiau Equationsmentioning

confidence: 99%

Duffin–Kemmer–Petiau and Dirac Equations—A Supersymmetric Connection

Okniński¹

2012

Symmetry

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Abstract:In the present paper we study subsolutions of the Dirac and Duffin-Kemmer-Petiau equations in the interacting case. It is shown that the Dirac equation in longitudinal external fields can be split into two covariant subequations (Dirac equations with built-in projection operators). Moreover, it is demonstrated that the Duffin-Kemmer-Petiau equations in crossed fields can be split into two 3 × 3 subequations. We show that all the subequations can be obtained via minimal coupling from the same 3 × 3 subequations which are thus a supersymmetric link between fermionic and bosonic degrees of freedom.

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“…with 5 × 5 and 10 × 10 matrices β µ , respectively, which fulfill the following commutation relations [26][27][28][29]:…”

Section: The Duffin-kemmer-petiau Equationsmentioning

confidence: 99%

Duffin–Kemmer–Petiau and Dirac Equations—A Supersymmetric Connection

Okniński¹

2012

Symmetry

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“…which enables to use the known results [5] connected with complete sets of irreducible KDP matrices. Using the classical Lie algorithm (see, e.g., references [6,7]), it is possible to prove that equations (1.3), (1.4) are invariant under a 6-parametrical Lie group, whose generators are…”

Section: Lie Symmetriesmentioning

confidence: 99%

“…Thus, denoting ψ = column(ψ (10) , ψ (5) , ψ (1) ) where ψ (10) , ψ (5) , ψ (1) are ten-, five-and one-component functions, we obtain from (1.3)…”

Section: Lie Symmetriesmentioning

confidence: 99%

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Symmetry Analysis of Nonlinear PDE with A "Mathematica" Program SYMMAN

Vorob'ev

1996

JNMP

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“…Eddington [22] spoke of "pure" E-numbers, but these were the principal idempotents and their "factorization" amounted to the construction of the symmetry adapted functions. A much more exhaustive treatment of this realm was given by HarishChandra [23] and Rao [24], the former also applying similar techniques [25] to the closely related Kemmer matrices [26]. Although Dirac's use of anticommuting operators in 1928 to factor a quadratic form into linear factors suggests a similar technique to be used for other forms, it was not until 1954 that Heerema [27] published a comprehensive analysis of the use of hypercomplex numbers to factor a binary cubic.…”

Section: Introductionmentioning

confidence: 99%

Symmetry adapted functions belonging to the dirac groups

Deepak

Dulock

Thomas

et al. 1969

Int J of Quantum Chemistry

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AbstractsAn earlier analysis of the canonical form of a pair of invertible operators obeying the exchange rule A B = w B Ais extended to cover a set of operators, between each pair of which a relation of this type exists; and for which a power of each operator is the unit matrix. Such relations define a system which may be regarded as a generalization of the Dirac matrices of relativistic quantum mechanics. We concentrate upon the group theoretic aspects of such a system and its matrix representations. Applications arise from the fact that all projective representations of finite abelian groups take the form of a Dirac Group. In particular, the representations of the magnetic space groups, which are projective representations of the lattice groups, arise in this manner.On gtntralise une analyse anttrieure de la forme canonique d'une paire d'optrateurs ayant des inverses et satisfaisant la relation A B = w B AA un ensemble d'optrateurs satisfaisant a une relation de ce type et pour lesquels une certaine puissance de chaque operateur est l'optrateur d'identitt. Ces relations dtfinissent un systeme qui peut Stre regardt comme une gtntralisation des matrices de Dirac dans la mtcanique quantique relativiste. Nous nous inttressons surtout aux aspects se rapportant a la thtorie des groupes. Des applications proviennent du fait que toutes les reprksentations projectives des groupes abtliens finis prennent la forme d'un groupe de Dirac. En particulier les reprtsentations des groupes d'espace magnttiques qui sont des representations projectives des groupes de rtseau, surgissent de cette facon-ci.

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The algebra of meson matrices

Abstract: In an interesting recent paper Schrödinger(5) contributes much new information on the properties of the hypercomplex algebra used in meson theory(1, 2, 4, 6, 7) which is defined by the relations(3)

Cited by 63 publications

References 6 publications

Duffin–Kemmer–Petiau and Dirac Equations—A Supersymmetric Connection

Duffin–Kemmer–Petiau and Dirac Equations—A Supersymmetric Connection

Symmetry Analysis of Nonlinear PDE with A "Mathematica" Program SYMMAN

Symmetry adapted functions belonging to the dirac groups

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