Event Generators for Discovery Physics
Review of Monte Carlo event generators for signals of new particles at LEP2. The areas covered include SUSY, HIGGS and Leptoquarks.
hep-ph↗
arXiv subjects
M. Jimbo
Publications and source records attributed to M. Jimbo.
Bilinear structure and Schlesinger transforms of the $q$-P$_{\rm III}$ and $q$-P$_{\rm VI}$ equations
We show that the recently derived ($q$-) discrete form of the Painlevé VI equation can be related to the discrete P$_{\rm III}$, in particular if one uses the full freedom in the implementation of the singularity confinement criterion. This observation is used here in order to derive the bilinear forms and the Schlesinger transformations of both $q$-P$_{\rm III}$ and $q$-P$_{\rm VI}$.
solv-int↗
New Level-0 Action of $U_q(\widehat{sl}_2)$ on Level-1 Modules
A level-0 action of $U_q(\widehat{sl}_2)$ is defined on the sum of level-1 irreducible highest weight modules. With the aid of the affine Hecke algebras, this action is realized on the basis created by the vertex operators. This is a $q$-analogue of the Yangian symmetry in conformal field theory.
q-alg↗
Level-0 structure of level-1 $U_q(\widehat{sl}_2)$-modules and Macdonald polynomials
The level-$1$ integrable highest weight modules of $U_q(\widehat{sl}_2)$ admit a level-$0$ action of the same algebra. This action is defined using the affine Hecke algebra and the basis of the level-$1$ module generated by components of vertex operators. Each level-$1$ module is a direct sum of finite-dimensional irreducible level-$0$ modules, whose highest weight vector is expressed in terms of Macdonald polynomials. This decomposition leads to the fermionic character formula for the level-$1$ modules.
q-alg↗
XXZ chain with a boundary
The $\XXZ$ spin chain with a boundary magnetic field $h$ is considered, using the vertex operator approach to diagonalize the Hamiltonian. We find explicit bosonic formulas for the two vacuum vectors with zero particle content. There are three distinct regions when $h\geq0$, in which the structure of the vacuum states is different. Excited states are given by the action of vertex operators on the vacuum states. We derive the boundary $S$-matrix and present an integral formula for the correlation functions. The boundary magnetization exhibits boundary hysteresis. We also discuss the rational limit, the $\XXX$ model.
hep-th↗
An elliptic quantum algebra for $\widehat{sl}_2$
An elliptic deformation of $\widehat{sl}_2$ is proposed. Our presentation of the algebra is based on the relation $RLL=LLR^*$, where $R$ and $R^*$ are eight-vertex $R$-matrices with the elliptic moduli chosen differently. In the trigonometric limit, this algebra reduces to a quotient of that proposed by Reshetikhin and Semenov-Tian-Shansky. Conjectures concerning highest weight modules and vertex operators are formulated, and the physical interpretation of $R^*$ is discussed.
hep-th↗
Notes on highest weight modules of the elliptic algebra ${\cal A}_{q,p}\left(\widehat{sl}_2\right)$
We discuss a construction of highest weight modules for the recently defined elliptic algebra ${\cal A}_{q,p}(\widehat{sl}_2)$, and make several conjectures concerning them. The modules are generated by the action of the components of the operator $L$ on the highest weight vectors. We introduce the vertex operators $Φ$ and $Ψ^*$ through their commutation relations with the $L$-operator. We present ordering rules for the $L$- and $Φ$-operators and find an upper bound for the number of linearly independent vectors generated by them, which agrees with the known characters of $\widehat{sl}_2$-modules.
hep-th↗
Smirnov's Integrals and Quantum Knizhnik-Zamolodchikov Equation of Level $0$
We study the quantum Knizhnik-Zamolodchikov equation of level $0$ associated with the spin $1/2$ representation of $U_q \bigl(\widehat{\frak s \frak l _{2}}\bigr)$. We find an integral formula for solutions in the case of an arbitrary total spin and $|q|<1$. In the formula, different solutions can be obtained by taking different integral kernels with the cycle of integration being fixed.
hep-th↗
Difference equations for the correlation functions of the eight vertex model
We propose that the correlation functions of the inhomogeneous eight vertex model in the anti-ferroelectric regime satisfy a system of difference equations with respect to the spectral parameters. Solving the simplest difference equation we obtain the expression for the spontaneous staggered polarization conjectured by Baxter and Kelland. We discuss also a related construction of vertex operators on the lattice.
hep-th↗