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.

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 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.

Symplectic Schrödinger equation for many-body systems

2020 ◽  
Vol 35 (06) ◽  
pp. 2050033
Author(s):  
R. G. G. Amorim ◽  
M. C. B. Fernandes ◽  
F. C. Khanna ◽  
A. E. Santana ◽  
J. D. M. Vianna
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fock Space ◽  
Basic Element ◽  
Space Representation ◽  
Many Body ◽  
Many Body Systems ◽  
The Green Function ◽  
Phase Space Representation

Using elements of symmetry, as gauge invariance, many aspects of a Schrödinger equation in phase space are analyzed. The number (Fock space) representation is constructed in phase space and the Green function, directly associated with the Wigner function, is introduced as a basic element of perturbative procedure. This phase space representation is applied to the Landau problem and the Liouville potential.

AN ANALYTICAL APPROACH TO THE FREDRICKSON–ANDERSEN MODEL WITH VACANCIES

1999 ◽  
Vol 13 (11) ◽  
pp. 1379-1396 ◽  
Author(s):  
C. PIGORSCH ◽  
M. SCHULZ ◽  
S. TRIMPER
Keyword(s):  
Ising Model ◽  
Fock Space ◽  
Supercooled Liquid ◽  
Space Representation ◽  
Kinetic Ising Model ◽  
Glass Forming ◽  
Andersen Model ◽  
Local Mobility ◽  
Glassy Materials ◽  
Three State Model

The dynamics of the n-spin facilitated kinetic Ising model (Fredrickson–Andersen model) with mobile vacancies as a model for the glassy materials are studied analytically by means of the Fock-space representation of the master equation. The system is mapped onto a three state model characterizing mobile, immobile and vacant cells. The characteristic cooperativity for glass forming systems are introduced by restrictions influencing the local dynamics and subsequently the local mobility of different lattice cells. In a moderate temperature regime the relaxation time versus the inverse temperature T-1 reveals two processes. Whereas the slow process can be identified with the conventional α-process of the supercooled liquid, the fast one originated by the additional empty sites is suggested to be the β JG -process due to Johari–Goldstein. The results are accordant with numerical simulations and suggest that the modified n-spin facilitated kinetic Ising model is able to describe qualitatively the behaviour of a supercooled liquid near the glass transition temperature T g .

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