Journal ArticleDOI
Para‐Bose and para‐Fermi operators as generators of orthosymplectic Lie superalgebras
TLDR
In this paper, the relative commutation relations between n pairs of Fermi operators and m pairs of Bose operators were defined in such a way that they generated the simple orthosymplectic Lie superalgebra B(n,m).Abstract:
It is shown that the relative commutation relations between n pairs of para‐Fermi operators and m pairs of para‐Bose operators can be defined in such a way that they generate the simple orthosymplectic Lie superalgebra B(n,m). In a case of ordinary statistics this leads to mutually anticommuting Bose and Fermi fields.read more
Citations
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Journal ArticleDOI
q-analogues of the parabose and parafermi oscillators and representations of quantum algebras
Roberto Floreanini,Luc Vinet +1 more
TL;DR: Deformations of one-dimensional parabose oscillators are presented in this paper and they are shown to provide Fock representations of the quantum sp q(2) algebra and ospq(1, 2) superalgebra.
Journal ArticleDOI
Once more on parastatistics
TL;DR: In this article, the equivalence between algebraic structures generated by parastatistics triple relations of Green (1953) and Greenberg-Messiah (1965) and certain orthosymplectic Lie superalgebras is found explicitly.
Journal ArticleDOI
Parastatistics as Lie-supertriple systems
TL;DR: In this paper, various new kinds of parastatistics discovered recently by Palev in addition to the standard one are reproduced and reformulated in terms of Lie-supertriple systems.
Journal ArticleDOI
Gel’fand–Zetlin basis and Clebsch–Gordan coefficients for covariant representations of the Lie superalgebra gl(m∣n)
TL;DR: A Gel'fand-Zetlin basis for the irreducible covariant tensor representations of the Lie superalgebra gl(m∣n) is introduced in this article.
Journal ArticleDOI
The quantum superalgebra Uq(osp(1/2n)): deformed para-Bose operators and root of unity representations
T. D. Palev,J. Van der Jeugt +1 more
TL;DR: In this article, the relation between the Lie superalgebra osp(1/2n) and para-Bose operators has been investigated and shown to be isomorphic to an associative algebra generated by so-called pre-oscillator operators satisfying a number of relations.
References
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Journal ArticleDOI
A Generalized Method of Field Quantization
TL;DR: In this article, it was shown that spin-half fields can be quantized in such a way that an arbitrary finite number of particles can exist in each eigenstate, and that the interchange of two particles of the same kind may or may not be physically significant, according to the type of interaction by means of which they are created or annihilated.
Journal ArticleDOI
Selection Rules for Parafields and the Absence of Para Particles in Nature
O.W. Greenberg,A.M.L. Messiah +1 more
Journal ArticleDOI
A generalization of field quantization and statistics
S. Kamefuchi,Yasushi Takahashi +1 more
TL;DR: In this article, an attempt is made at generalizing commutation relations of creation and annihilation operators in field theory, and the algebra for these operators is determined in such a way that they form a basis of representations of either an infinite-dimensional rotation group (R-type) or an infinitely-dimensional symplectic group (S-type).
Journal ArticleDOI
A Lie superalgebraic interpretation of the para‐Bose statistics
A. Ch. Ganchev,T. D. Palev +1 more
TL;DR: In this paper, it was shown that n pairs of para-Bose operators generate the simple orthosymplectic Lie superalgebra osp(1,2n) ≡B (0,n).