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

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

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

Field theories on spaces with linear fuzziness

A noncommutative space is considered the position operators of which satisfy the commutativity relations of a Lie algebra. The basic tools for calculation on this space, including the product of the fields, inner product and the proper measure for integration are derived. Some general aspects of perturbative field theory calculations on this space are also discussed. Among the features of such models is that they are free from ultraviolet divergences (and hence free from UV/IR mixing as well), if the group is compact. The example of the group SO(3) or SU(2) is investigated in more detail.Comment: 12 pages, no figs., LaTeX. v2: Comments and discussions are added, e.g. on absence of UV/IR phenomena. No change in result

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

Large-N limit of the generalized 2-dimensional Yang-Mills theories

Using the standard saddle-point method, we find an explicit relation for the large-N limit of the free energy of an arbitrary generalized 2D Yang-Mills theory in the weak ($AA_c$) region, we investigate carefully the specific fourth Casimir theory, and show that the ordinary integral equation of the density function is not adequate to find the solution. There exist, however, another equation which restricts the parameters. So one can find the free energy in strong region and show that the theory has a third order phase transition.Comment: 10 pages, minor typos corrected, one reference update

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