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

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.

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 Lebesgue Decomposition of Non-Commutative Measures

2020 ◽  
Author(s):  
Michael T Jury ◽  
Robert T W Martin
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Fock Space ◽  
Reproducing Kernel Hilbert Space ◽  
Semigroup Algebra ◽  
Space Theory ◽  
Lebesgue Decomposition ◽  
Sesquilinear Forms ◽  
Positive Linear Functionals ◽  
Algebra Theory

Abstract We extend the Lebesgue decomposition of positive measures with respect to Lebesgue measure on the complex unit circle to the non-commutative (NC) multi-variable setting of (positive) NC measures. These are positive linear functionals on a certain self-adjoint subspace of the Cuntz–Toeplitz $C^{\ast }-$algebra, the $C^{\ast }-$algebra of the left creation operators on the full Fock space. This theory is fundamentally connected to the representation theory of the Cuntz and Cuntz–Toeplitz $C^{\ast }-$algebras; any *−representation of the Cuntz–Toeplitz $C^{\ast }-$algebra is obtained (up to unitary equivalence), by applying a Gelfand–Naimark–Segal construction to a positive NC measure. Our approach combines the theory of Lebesgue decomposition of sesquilinear forms in Hilbert space, Lebesgue decomposition of row isometries, free semigroup algebra theory, NC reproducing kernel Hilbert space theory, and NC Hardy space theory.

Toeplitz Operators on the Fock Space with Presymbols Discontinuous on a Thick Set

1996 ◽  
Vol 180 (1) ◽  
pp. 299-315 ◽  
Author(s):  
E. Ram Írez De Arellano ◽  
N. L. Vasilevski
Keyword(s):  
Toeplitz Operators ◽  
Fock Space

scholarly journals Singular Bogoliubov transformations and inequivalent representations of canonical commutation relations

2019 ◽  
Vol 31 (08) ◽  
pp. 1950026 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Fock Space ◽  
Sufficient Conditions ◽  
Bogoliubov Transformation ◽  
Fock Representation ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Direct Sum ◽  
Boson Fock Space ◽  
Inequivalent Representations ◽  
Bogoliubov Transformations

We introduce a concept of singular Bogoliubov transformation on the abstract boson Fock space and construct a representation of canonical commutation relations (CCRs) which is inequivalent to any direct sum of the Fock representation. Sufficient conditions for the representation to be irreducible are formulated. Moreover, an example of such representations of CCRs is given.

scholarly journals Interpolation and sampling hypersurfaces for the Bargmann-Fock space in higher dimensions

2006 ◽  
Vol 335 (1) ◽  
pp. 79-107 ◽  
Author(s):  
Joaquim Ortega-Cerdà ◽  
Alexander Schuster ◽  
Dror Varolin
Keyword(s):  
Fock Space ◽  
Higher Dimensions

Coupled-cluster method in Fock space. II. Brueckner-Hartree-Fock method

1985 ◽  
Vol 32 (2) ◽  
pp. 743-747 ◽  
Author(s):  
Leszek Z. Stolarczyk ◽  
Hendrik J. Monkhorst
Keyword(s):  
Fock Space ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Coupled Cluster Method ◽  
Hartree Fock
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