scholarly journals N-point matrix elements of dynamical vertex operators of the higher spin XXZ model

1995 ◽  
Vol 28 (20) ◽  
pp. 5831-5842 ◽  
Author(s):  
A H Bougourzi
Keyword(s):  
Vertex Operators ◽  
Matrix Elements ◽  
Xxz Model ◽  
Higher Spin

scholarly journals A LECTURE ON THE LIOUVILLE VERTEX OPERATORS (REVIEW)

2004 ◽  
Vol 19 (supp02) ◽  
pp. 436-458 ◽  
Author(s):  
J. TESCHNER
Keyword(s):  
Free Field ◽  
Liouville Theory ◽  
Vertex Operators ◽  
Continuous Family ◽  
Matrix Elements ◽  
Crossing Symmetry ◽  
The Matrix

We reconsider the construction of exponential fields in the quantized Liouville theory. It is based on a free-field construction of a continuous family or chiral vertex operators. We derive the fusion and braid relations of the chiral vertex operators. This allows us to simplify the verification of locality and crossing symmetry of the exponential fields considerably. The calculation of the matrix elements of the exponential fields leads to a constructive derivation of the formula proposed by Dorn/Otto and the brothers Zamolodchikov.

FUSION CONSTRUCTION OF THE VERTEX OPERATORS IN HIGHER LEVEL REPRESENTATION OF THE ELLIPTIC QUANTUM GROUP

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1995-2001
Author(s):  
HITOSHI KONNO
Keyword(s):  
Quantum Group ◽  
Free Field ◽  
Vertex Operators ◽  
Type I ◽  
Field Representation ◽  
Short Summary ◽  
Higher Spin ◽  
Elliptic Algebra ◽  
Elliptic Quantum ◽  
Weight Coefficients

After a short summary on the elliptic quantum group [Formula: see text] and the elliptic algebra [Formula: see text], we present a free field representation of the Drinfeld currents and the vertex operators (VO's) in the level k. We especially demonstrate a construction of the higher spin type I VO's by fusing the spin 1/2 type I VO's and fix a rule of attaching the screening current S(z) associated with the q-deformed ℤk-parafermion theory. As a result we get a free field representation of the higher spin type I VO's which commutation relation by the fused Boltzmann weight coefficients is manifest.

SOME INTEGRAL FORMULAS FOR THE SOLUTIONS OF THE sl2 dKZ EQUATION WITH LEVEL −4

1994 ◽  
Vol 09 (32) ◽  
pp. 5673-5687 ◽  
Author(s):  
ATSUSHI NAKAYASHIKI
Keyword(s):  
Correlation Function ◽  
Integral Formula ◽  
Time Integration ◽  
Direct Proof ◽  
Vertex Operators ◽  
Type I ◽  
Xxz Model ◽  
Integral Formulas ◽  
Xxx Model

A direct proof is given for the fact that the integral formula for the XXX limit of the trace of the type I q-vertex operators satisfies the deformed Knizhnik-Zamolodchikov (dKZ) equation with level −4. We have also carried out one-time integration by taking the residue at infinity. As a corollary of these we can construct a family of the integral formulas for solutions to the dKZ equation. Another corollary is the integral formula for the correlation function of the inhomogeneous XXX model, whose number of integrals is less than that of the previously obtained correlator for the XXZ model.

scholarly journals MATRIX ELEMENTS OF Uq[su(2)k] VERTEX OPERATORS VIA BOSONIZATION

1994 ◽  
Vol 09 (25) ◽  
pp. 4431-4447 ◽  
Author(s):  
A. H. BOUGOURZI ◽  
ROBERT A. WESTON
Keyword(s):  
Vertex Operators ◽  
Matrix Elements ◽  
Point Function ◽  
Single Integral ◽  
Kz Equation ◽  
Arbitrary Level

We construct bosonized vertex operators (VO's) and conjugate vertex operators (CVO's) of Uq[ su (2)k] for arbitrary level k and representation j ≤ k/2. Both are obtained directly as two solutions of the defining condition of vertex operators — namely that they intertwine Uq[ su (2)k] modules. We construct the screening charge and present a formula for the n-point function. Specializing to j = 1/2 we construct all VO's and CVO's explicitly. The existence of the CVO allows us to place the calculation of the two-point function on the same footing as k = 1; that is, it is obtained without screening currents and involves only a single integral from the CVO. This integral is evaluated and the resulting function is shown to obey the q-KZ equation and to reduce simply to both the expected k = 1 and q = 1 limits.

scholarly journals ANNIHILATION POLES FOR FORM FACTORS IN THE XXZ MODEL

1994 ◽  
Vol 09 (12) ◽  
pp. 2087-2102 ◽  
Author(s):  
S. PAKULIAK
Keyword(s):  
Form Factor ◽  
Linear Combination ◽  
Form Factors ◽  
Vertex Operators ◽  
Xxz Model ◽  
Particle Form

The annihilation poles for the form factors in the XXZ model are studied using vertex operators introduced in Ref. 1. An annihilation pole is the property of form factors according to which the residue of the 2n-particle form factor in such a pole can be expressed through linear combination of the (2n−2)-particle form factors. To prove this property we use the bosonization of the vertex operators in the XXZ model which was invented in Ref. 2.

Covariant higher spin vertex operators in the Ramond sector

1987 ◽  
Vol 292 ◽  
pp. 201-221 ◽  
Author(s):  
I.G. Koh ◽  
W. Troost ◽  
A. Van Proeyen
Keyword(s):  
Vertex Operators ◽  
Higher Spin

scholarly journals On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model

2021 ◽  
Author(s):  
Hao Pei ◽  
Veronique Terras
Keyword(s):  
Boundary Conditions ◽  
Transfer Matrix ◽  
Separation Of Variables ◽  
Form Factors ◽  
Periodic Case ◽  
Matrix Elements ◽  
Heisenberg Chain ◽  
Xxz Model ◽  
Matrix Eigenvalues ◽  
Scalar Products

Abstract We consider the XXZ spin-1/2 Heisenberg chain with antiperiodic boundary conditions. The inhomogeneous version of this model can be solved by Separation of Variables (SoV), and the eigenstates can be constructed in terms of Q-functions, solution of a Baxter TQ-equation, which have double periodicity compared to the periodic case. We compute in this framework the scalar products of a particular class of separate states which notably includes the eigenstates of the transfer matrix. We also compute the form factors of local spin operators, i.e. their matrix elements between two eigenstates of the transfer matrix. We show that these quantities admit determinant representations with rows and columns labelled by the roots of the Q-functions of the corresponding separate states, as in the periodic case, although the form of the determinant are here slightly different. We also propose alternative types of determinant representations written directly in terms of the transfer matrix eigenvalues.

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