scholarly journals Fock space representation of differential calculus on the noncommutative quantum space

1997 ◽  
Vol 38 (1) ◽  
pp. 466-475 ◽  
Author(s):  
A. K. Mishra ◽  
G. Rajasekaran
Keyword(s):  
Differential Calculus ◽  
Fock Space ◽  
Space Representation ◽  
Quantum Space ◽  
Noncommutative Quantum

Exploring Representation Theory of Unitary Groups via Linear Optical Passive Devices

2006 ◽  
Vol 13 (04) ◽  
pp. 415-426 ◽  
Author(s):  
P. Aniello ◽  
C. Lupo ◽  
M. Napolitano
Keyword(s):  
Lie Algebras ◽  
Fock Space ◽  
Fixed Number ◽  
Unitary Groups ◽  
Space Representation ◽  
Remarkable Case ◽  
Mathematical Structures ◽  
Passive Devices ◽  
Optical Modes ◽  
Linear Optical

In this paper, we investigate some mathematical structures underlying the physics of linear optical passive (LOP) devices. We show, in particular, that with the class of LOP transformations on N optical modes one can associate a unitary representation of U (N) in the N-mode Fock space, representation which can be decomposed into irreducible sub-representations living in the subspaces characterized by a fixed number of photons. These (sub-)representations can be classified using the theory of representations of semi-simple Lie algebras. The remarkable case where N = 3 is studied in detail.

scholarly journals CONSISTENT DEFORMED BOSONIC ALGEBRA IN NONCOMMUTATIVE QUANTUM MECHANICS

2008 ◽  
Vol 23 (09) ◽  
pp. 1393-1403 ◽  
Author(s):  
JIAN-ZU ZHANG
Keyword(s):  
Quantum Mechanics ◽  
Weyl Algebra ◽  
Fock Space ◽  
General Relation ◽  
Noncommutative Space ◽  
Two Dimensional ◽  
Noncommutative Quantum Mechanics ◽  
Commutative Space ◽  
Creation Operators ◽  
Noncommutative Quantum

In two-dimensional noncommutative space for the case of both position–position and momentum–momentum noncommuting, the consistent deformed bosonic algebra at the nonperturbation level described by the deformed annihilation and creation operators is investigated. A general relation between noncommutative parameters is fixed from the consistency of the deformed Heisenberg–Weyl algebra with the deformed bosonic algebra. A Fock space is found, in which all calculations can be similarly developed as if in commutative space and all effects of spatial noncommutativity are simply represented by parameters.

scholarly journals A TWO-PARAMETER DEFORMED SUSY ALGEBRA FOR SUp/q(n)-COVARIANT (p,q)-DEFORMED FERMIONIC OSCILLATORS

2005 ◽  
Vol 20 (08) ◽  
pp. 613-622 ◽  
Author(s):  
ABDULLAH ALGIN ◽  
METIN ARIK
Keyword(s):  
Quantum Group ◽  
Fock Space ◽  
Space Representation ◽  
Oscillator Algebra ◽  
Two Parameter

We construct a two-parameter deformed SUSY algebra by constructing SUSY generators which are bilinears of n (p,q)-deformed fermions covariant under the quantum group SU p/q(n) and n undeformed bosons. The Fock space representation of the algebra constructed is discussed and the total deformed Hamiltonian for such a system is obtained. Some physical applications of the quantum group covariant two-parameter deformed fermionic oscillator algebra are also considered.

ON THE FOCK SPACE REPRESENTATION OF THE WITTEN VERTEX

1994 ◽  
Vol 09 (06) ◽  
pp. 465-477
Author(s):  
RAINER DICK
Keyword(s):  
Closed Form ◽  
Fock Space ◽  
Closed String ◽  
Space Representation ◽  
Operator Representations

The bosonic overlap conditions for operator representations of the Witten vertex and its closed string analog are solved in closed form for arbitrary many external strings. This is accomplished by the use of transformed operator bases of the strings. In particular, the bosonic factor of the Witten vertex for three closed strings is realized in Fock space.

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