Derivation of theories: structures of the derived system in terms of those of the original system in classical mechanics

We present the technique of derivation of a theory to obtain an $(n+1)f$-degrees-of-freedom theory from an $f$-degrees-of-freedom theory and show that one can calculate all of the quantities of the derived theory from those of the original one. Specifically, we show that one can use this technique to construct, from an integrable system, other integrable systems with more degrees of freedom.Comment: LaTex, 10 page

A pseudo-conformal representation of the Virasoro algebra

Generalizing the concept of primary fields, we find a new representation of the Virasoro algebra, which we call it a pseudo-conformal representation. In special cases, this representation reduces to ordinary- or logarithmic-conformal field theory. There are, however, other cases in which the Green functions differ from those of ordinary- or logarithmic-conformal field theories. This representation is parametrized by two matrices. We classify these two matrices, and calculate some of the correlators for a simple example.Comment: LaTex, 5 page

The universal R-matrix for the Jordanian deformation of sl(2), and the contracted forms of so(4)

We introduce a universal R matrix for the Jordanian deformation of \U{ \sl(2)}. Using \Uh{\so(4)}=\Uh{\sl(2)} \oplus {\rm U}_{-h}(\sl(2)), we obtain the universal R matrix for \Uh{\so(4)}. Applying the graded contractions on the universal R matrix of \Uh{\so(4)}, we show that there exist three distinct R matrices for all of the contracted algebras. It is shown that \Uh{\sl(2)}, \Uh{\so(4)}, and all of these contracted algebras are triangular.Comment: LaTeX, 8 page

Models solvable through the empty-interval method

The most general one dimensional reaction-diffusion model with nearest-neighbor interactions solvable through the empty interval method, and without any restriction on the particle-generation from two adjacent empty sites is studied. It is shown that turning on the reactions which generate particles from two adjacent empty sites, results in a gap in the spectrum of the evolution operator (or equivalently a finite relaxation time).Comment: 8 page

A Triangular Deformation of the two Dimensional Poincare Algebra

Contracting the $h$-deformation of \SL(2,\Real), we construct a new deformation of two dimensional Poincar\'e algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is triangular, and its universal R matrix is also constructed explicitly. Then, we find a deformation map for the universal enveloping algebra, and at the end, give the deformed mass shells and Lorentz transformation.Comment: 11 pages, LaTeX, Two figures upon reques

Derivation of quantum theories:symmetries and the exact solution of the derived system

Based on the technique of derivation of a theory, presented in our recent paper, we investigate the properties of the derived quantum system. We show that the derived quantum system possesses the (nonanomalous) symmetries of the original one, and prove that the exact Green functions of the derived theory are expressed in terms of the semiclassically approximated Green functions of the original theory.Comment: 8 pages,LaTe

Nonuniform autonomous one-dimensional exclusion nearest-neighbor reaction-diffusion models

The most general nonuniform reaction-diffusion models on a one-dimensional lattice with boundaries, for which the time evolution equations of corre- lation functions are closed, are considered. A transfer matrix method is used to find the static solution. It is seen that this transfer matrix can be obtained in a closed form, if the reaction rates satisfy certain conditions. We call such models superautonomous. Possible static phase transitions of such models are investigated. At the end, as an example of superau- tonomous models, a nonuniform voter model is introduced, and solved explicitly.Comment: 14 page

Logarithmic conformal field theories with continuous weights

We study the logarithmic conformal field theories in which conformal weights are continuous subset of real numbers. A general relation between the correlators consisting of logarithmic fields and those consisting of ordinary conformal fields is investigated. As an example the correlators of the Coulomb-gas model are explicitly studied.Comment: Latex, 12 pages, IPM preprint, to appear in Phys. Lett.