A Bose description of the 1-D para-Bose and para-Fermi oscillators

2009 ◽  
Vol 87 (6) ◽  
pp. 619-624
Author(s):  
Ramón J. Cova
Keyword(s):  
Fock Space ◽  
Irreducible Representations ◽  
Straight Lines ◽  
Bose Operators

In the Fock space of two Bose operators all the irreducible representations of both the 1-D para-Bose and para-Fermi oscillators are constructed. Bose states of the form |p + k–1, kn > (|p – k, kn), n = 1,2, are shown to stand for states of k-parabosons (k-parafermions) of order p. For n = 1 or n = 2 the various subspaces may be visualized in the plane as either straight-lines or parabolae, respectively.

The Paraboson Fock Space and Unitary Irreducible Representations of the Lie Superalgebra $${\mathfrak{osp}(1|2n)}$$

2008 ◽  
Vol 281 (3) ◽  
pp. 805-826 ◽  
Author(s):  
S. Lievens ◽  
N. I. Stoilov ◽  
J. Van der Jeugt
Keyword(s):  
Fock Space ◽  
Lie Superalgebra ◽  
Irreducible Representations

Irreducible representations of para-Bose operators

1972 ◽  
Vol 10 (3) ◽  
pp. 499-512
Author(s):  
C. Alabiso ◽  
F. Duimio
Keyword(s):  
Irreducible Representations ◽  
Bose Operators

Realisations of the representations of para-Fermi algebra in Fock space of Bose operators: part II

1970 ◽  
Vol 3 (2) ◽  
pp. 115-118 ◽  
Author(s):  
K. Kademova ◽  
A. J. Kálnay
Keyword(s):  
Fock Space ◽  
Bose Operators

scholarly journals Dual pair correspondence in physics: oscillator realizations and representations

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Thomas Basile ◽  
Euihun Joung ◽  
Karapet Mkrtchyan ◽  
Matin Mojaza
Keyword(s):  
Closed Form ◽  
Fock Space ◽  
Dual Pair ◽  
Irreducible Representations ◽  
Systematic Treatment ◽  
Dual Pairs ◽  
Howe Duality ◽  
Casimir Operators ◽  
General Aspects ◽  
Dual Pair Correspondence

Abstract We study general aspects of the reductive dual pair correspondence, also known as Howe duality. We make an explicit and systematic treatment, where we first derive the oscillator realizations of all irreducible dual pairs: (GL(M, ℝ), GL(N, ℝ)), (GL(M, ℂ), GL(N, ℂ)), (U∗(2M), U∗(2N)), (U (M+, M−), U (N+, N−)), (O(N+, N−), Sp (2M, ℝ)), (O(N, ℂ), Sp(2M, ℂ)) and (O∗(2N ), Sp(M+, M−)). Then, we decompose the Fock space into irreducible representations of each group in the dual pairs for the cases where one member of the pair is compact as well as the first non-trivial cases of where it is non-compact. We discuss the relevance of these representations in several physical applications throughout this analysis. In particular, we discuss peculiarities of their branching properties. Finally, closed-form expressions relating all Casimir operators of two groups in a pair are established.

scholarly journals The Paraboson Fock Space and Unitary Irreducible Representations of the Lie Superalgebra $${{\mathfrak{osp}}}$$ (1|2n)

2008 ◽  
Vol 282 (2) ◽  
pp. 575-575 ◽  
Author(s):  
S. Lievens ◽  
N. I. Stoilova ◽  
J. Van der Jeugt
Keyword(s):  
Fock Space ◽  
Lie Superalgebra ◽  
Irreducible Representations

Generalized Bose Operators in the Fock Space of a Single Bose Operator

1969 ◽  
Vol 10 (7) ◽  
pp. 1168-1176 ◽  
Author(s):  
Richard A. Brandt ◽  
O. W. Greenberg
Keyword(s):  
Fock Space ◽  
Bose Operator ◽  
Bose Operators

scholarly journals CLIFFORD MODULES AND SYMMETRIES OF TOPOLOGICAL INSULATORS

2012 ◽  
Vol 09 (03) ◽  
pp. 1250023 ◽  
Author(s):  
GILLES ABRAMOVICI ◽  
PAVEL KALUGIN
Keyword(s):  
Clifford Algebras ◽  
Fock Space ◽  
Irreducible Representations ◽  
Fermion Systems ◽  
Symmetry Classes ◽  
Dual Object ◽  
Clifford Module ◽  
Clifford Modules ◽  
Symmetry Constraints

We complete the classification of symmetry constraints on gapped quadratic fermion hamiltonians proposed by Kitaev. The symmetry group is supposed compact and can include arbitrary unitary or antiunitary operators in the Fock space that conserve the algebra of quadratic observables. We analyze the multiplicity spaces of real irreducible representations of unitary symmetries in the Nambu space. The joint action of intertwining operators and antiunitary symmetries provides these spaces with the structure of Clifford module: we prove a one-to-one correspondence between the ten Altland–Zirnbauer symmetry classes of fermion systems and the ten Morita equivalence classes of real and complex Clifford algebras. The antiunitary operators, which occur in seven classes, are projectively represented in the Nambu space by unitary "chiral symmetries". The space of gapped symmetric hamiltonians is homotopically equivalent to the product of classifying spaces indexed by the dual object of the group of unitary symmetries.

Realisations of the representations of para-Fermi algebra in Fock space of Bose operators: part I

1970 ◽  
Vol 3 (2) ◽  
pp. 109-114 ◽  
Author(s):  
K. Kademova
Keyword(s):  
Fock Space ◽  
Bose Operators

scholarly journals BRST ANALYSIS OF N=2 SUPERCONFORMAL MINIMAL UNITARY MODELS IN COULOMB GAS FORMALISM

1994 ◽  
Vol 09 (32) ◽  
pp. 5821-5848
Author(s):  
KATSUYUKI SUGIYAMA
Keyword(s):  
Fock Space ◽  
Coulomb Gas ◽  
Superconformal Algebra ◽  
Character Formula ◽  
Irreducible Representations ◽  
Brst Cohomology

We perform a BRST analysis of the N=2 superconformal minimal unitary models. A bosonic as well as fermionic BRST operators are used to construct irreducible representations of the N=2 superconformal algebra on the Fock space as BRST cohomology classes of the BRST operators. Also a character formula is rederived by using the BRST analysis.

Domain Formation in Synthetic Quartz

1971 ◽  
Vol 29 ◽  
pp. 156-157
Author(s):  
Joseph J. Comer
Keyword(s):  
Electron Beam ◽  
Room Temperature ◽  
Domain Formation ◽  
Synthetic Quartz ◽  
Transmission Electron ◽  
Black Spots ◽  
Diffraction Mode ◽  
Domain Boundaries ◽  
Kikuchi Lines ◽  
Straight Lines

Domains visible by transmission electron microscopy, believed to be Dauphiné inversion twins, were found in some specimens of synthetic quartz heated to 680°C and cooled to room temperature. With the electron beam close to parallel to the [0001] direction the domain boundaries appeared as straight lines normal to <100> and <410> or <510> directions. In the selected area diffraction mode, a shift of the Kikuchi lines was observed when the electron beam was made to traverse the specimen across a boundary. This shift indicates a change in orientation which accounts for the visibility of the domain by diffraction contrast when the specimen is tilted. Upon exposure to a 100 KV electron beam with a flux of 5x 1018 electrons/cm2sec the boundaries are rapidly decorated by radiation damage centers appearing as black spots. Similar crystallographio boundaries were sometimes found in unannealed (0001) quartz damaged by electrons.

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