相关论文: $\tau$-function within group theory approach and i…
A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique…
We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.
This is a review of the authors' recent results on an integrable structure of the melting crystal model with external potentials. The partition function of this model is a sum over all plane partitions (3D Young diagrams). By the method of…
The main aim of this work is to relate integrability in QFT with a complete particle interpretation directly to the principle of causal localization, circumventing the standard method of finding sufficiently many conservation laws. Its…
We collect and systematize general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems. As an example, we reconsider the case of the quantum group…
We introduce the group field theory (GFT) formalism for non-perturbative quantum gravity, and present it as a potential unifying framework for several other quantum gravity approaches, i.e. loop quantum gravity and simplicial quantum…
Integrability in quantum theory has been defined in more than one ways. Recently, Braak suggested a new definition that a quantum system is integrable if the number of parameters required to specify the eigenstates and the number degrees of…
Relations between differential calculi, quantum groups, integrable systems, and q-analysis are studied. Some new Hirota type formulas are established for qKP along with variations on classical Hirota formulas.
This paper presents the theory of Bohr-Sommerfeld-Heisenberg quantization of a completely integrable Hamiltonian system in the context of geometric quantization. The theory is illustrated with several examples.
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
We develop a formal group--theoretic framework for the Riemann zeta function by treating its Euler product as an element of the multiplicative formal group $\widehat{\mathbb{G}}_m$ and its logarithm as the associated formal group logarithm.…
We give a systematic, abstract formulation of the image normalization method as applied to a general group of image transformations, and then illustrate the abstract analysis by applying it to the hierarchy of viewing transformations of a…
Recent work on Euler hierarchies of field theory Lagrangians iteratively constructed {}from their successive equations of motion is briefly reviewed. On the one hand, a certain triality structure is described, relating arbitrary field…
An elliptic version of quantum groups is proposed. It comes form the quantization of the Knizhnik-Zamolodchikov- Bernard equation on the torus. The relation with elliptic IRF models is explained.
We canonically quantize the tau-functions for the birational Weyl group action arising from a nilpotent Poisson algebra proposed by Noumi and Yamada. We also construct the q-difference deformation of the canonical quantization of the…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in…