212 research outputs found
Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality
The quantum discrete Liouville model in the strongly coupled regime, 1<c<25,
is formulated as a well defined quantum mechanical problem with unitary
evolution operator. The theory is self-dual: there are two exponential fields
related by Hermitean conjugation, satisfying two discrete quantum Liouville
equations, and living in mutually commuting subalgebras of the quantum algebra
of observables.Comment: Latex2e, 20 page
Finite-dimensional analogs of string s <-> t duality and pentagon equation
We put forward one of the forms of functional pentagon equation (FPE), known
from the theory of integrable models, as an algebraic explanation to the
phenomenon known in physics as st duality. We present two simple geometrical
examples of FPE solutions, one of them yielding in a particular case the
well-known Veneziano expression for 4-particle amplitude. Finally, we interpret
our solutions of FPE in terms of relations in Lie groups.Comment: LaTeX, 12 pages, 6 eps figure
Multidimensional analogs of geometric s<-->t duality
The usual propetry of st duality for scattering amplitudes, e.g. for
Veneziano amplitude, is deeply connected with the 2-dimensional geometry. In
particular, a simple geometric construction of such amplitudes was proposed in
a joint work by this author and S.Saito (solv-int/9812016). Here we propose
analogs of one of those amplitudes associated with multidimensional euclidean
spaces, paying most attention to the 3-dimensional case. Our results can be
regarded as a variant of "Regge calculus" intimately connected with ideas of
the theory of integrable models.Comment: LaTeX2e, pictures using emlines. In this re-submission, an English
version of the paper is added (9 pages, file english.tex) to the originally
submitted file in Russian (10 pages, russian.tex
On the relation between quantum Liouville theory and the quantized Teichm"uller spaces
We review both the construction of conformal blocks in quantum Liouville
theory and the quantization of Teichm\"uller spaces as developed by Kashaev,
Checkov and Fock. In both cases one assigns to a Riemann surface a Hilbert
space acted on by a representation of the mapping class group. According to a
conjecture of H. Verlinde, the two are equivalent. We describe some key steps
in the verification of this conjecture.Comment: Contribution to the proceedings of the 6th International Conference
on CFTs and Integrable Models, Chernogolovka, Russia, September 2002; v2:
Typos corrected, typographical change
Three-Dimensional Integrable Models and Associated Tangle Invariants
In this paper we show that the Boltzmann weights of the three-dimensional
Baxter-Bazhanov model give representations of the braid group, if some suitable
spectral limits are taken. In the trigonometric case we classify all possible
spectral limits which produce braid group representations. Furthermore we prove
that for some of them we get cyclotomic invariants of links and for others we
obtain tangle invariants generalizing the cyclotomic ones.Comment: Number of pages: 21, Latex fil
--Geometry and Associated Continuous Toda System
We discuss an infinite--dimensional k\"ahlerian manifold associated with the
area--preserving diffeomorphisms on two--dimensional torus, and,
correspondingly, with a continuous limit of the --Toda system. In
particular, a continuous limit of the --Grassmannians and a related
Pl\"ucker type formula are introduced as relevant notions for
--geometry of the self--dual Einstein space with the rotational
Killing vector.Comment: 6 pages, no figure report\# ETH-TH/93-2
The vertex formulation of the Bazhanov-Baxter Model
In this paper we formulate an integrable model on the simple cubic lattice.
The -- valued spin variables of the model belong to edges of the lattice.
The Boltzmann weights of the model obey the vertex type Tetrahedron Equation.
In the thermodynamic limit our model is equivalent to the Bazhanov -- Baxter
Model. In the case when we reproduce the Korepanov's and Hietarinta's
solutions of the Tetrahedron equation as some special cases.Comment: 20 pages, LaTeX fil
Correlation between NMR parameters and performance of bitumen. Role of structure ordering
Parameters of nuclear magnetic relaxation (spin-spin relaxation times, corresponding proton concentrations P i) have been measured for initial and oxidized bitumen from Tatarstan oils. It is shown that pulse nuclear magnetic resonance method allows to analyze the bitumen composition by phases with different molecular mobility of hydrocarbons and proton concentrations P i
A Symmetric Generalization of Linear B\"acklund Transformation associated with the Hirota Bilinear Difference Equation
The Hirota bilinear difference equation is generalized to discrete space of
arbitrary dimension. Solutions to the nonlinear difference equations can be
obtained via B\"acklund transformation of the corresponding linear problems.Comment: Latex, 12 pages, 1 figur
- …