scholarly journals Vertex operator in String Theory on Orbifold: Intertwining Fields between Different Sectors in the Fock Space Representation

1987 ◽  
Vol 77 (3) ◽  
pp. 731-750
Author(s):  
H. Muratani
Keyword(s):  
String Theory ◽  
Vertex Operator ◽  
Fock Space ◽  
Space Representation

ABELIZED VIRASORO OPERATORS, GEOMETRY AND THE STRING VERTEX OPERATOR

1989 ◽  
Vol 04 (14) ◽  
pp. 3503-3575 ◽  
Author(s):  
HENRIK ARATYN ◽  
RANDALL INGERMANSON
Keyword(s):  
String Theory ◽  
Vertex Operator ◽  
Fock Space ◽  
Photon Emission ◽  
Central Element ◽  
Algebraic Approach ◽  
Global Symmetry ◽  
Extended Phase ◽  
Simple Method ◽  
Constrained Hamiltonian Systems

In this article, we review recent work on constrained Hamiltonian systems with infinite-dimensional constraint algebras. The work is based on an extension of the constraint algebra to include subsidiary (gauge-fixing) constraints and a central element, forming a larger, closed algebra. This extension leads to several immediate results, at both a practical and a conceptual level: 1) A simple method is found for abelizing the original constraints. 2) This leads naturally to a “generalized vielbein” relating Abelian and non-Abelian quantities. 3) The vielbein apparatus makes transparent the full global symmetry of the extended phase space associated with the Batalin, Fradkin and Vilkovisky formalism. An interesting duality also arises between quantities with “Abelian” and “non-Abelian” indices. String theory provides the most important and straightforward application of these general methods. For this special case, one finds that the vielbeins are the Fourier components of the string vertex operator. The vertex operator describes the physical process of photon emission, and determines the physical modes of the string by way of the DDF operators. Due to the relation between the vertex operator and the vielbein, the dual abelized Virasoro operators simplify the usual discussion of the physical Fock space. The correspondence between these two fundamental objects, the vertex and the vielbein, thus provides a geometric understanding of the usual algebraic approach to string theory.

q-DEFORMED W-ALGEBRA FROM q-FERMION OSCILLATORS AND THE ALGEBRAIC STRUCTURE OF VERTEX OPERATORS IN 2D STRING THEORY

2002 ◽  
Vol 17 (07) ◽  
pp. 399-411 ◽  
Author(s):  
R. PARTHASARATHY
Keyword(s):  
String Theory ◽  
Algebraic Structure ◽  
Fock Space ◽  
Higher Order ◽  
Space Representation ◽  
Vertex Operators

q-deformed fermion oscillators are used to construct q-deformed higher order Virasaro algebra in the Fock space representation. These facilitate the realization of q-deformed W∞-algebra. The vertex operators (positively dressed) in 2D string theory are interpreted in terms of q-fermionic states.

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.

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.

scholarly journals THE ANYON MODEL: AN EXAMPLE INSPIRED BY STRING THEORY

2011 ◽  
Vol 26 (16) ◽  
pp. 2757-2772 ◽  
Author(s):  
S. V. TALALOV
Keyword(s):  
Dynamical System ◽  
Energy Spectrum ◽  
String Theory ◽  
Arbitrary Number ◽  
Simple Formula ◽  
Fock Space ◽  
Space Time ◽  
Fermionic Field ◽  
Spectral Problems

We investigate the enlarged class of open finite strings in (2+1)D space–time. The new dynamical system related to this class is constructed and quantized here. As the result, the energy spectrum of the model is defined by a simple formula [Formula: see text]; the spin [Formula: see text] is an arbitrary number here but the constants αn and cn are eigenvalues for certain spectral problems in fermionic Fock space Hψ constructed for the free 2D fermionic field.

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