Related papers: Rogers dilogarithm in integrable systems
We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety : the regular functions and the continuous rational functions.
This is an expanded version of the notes by the second author of the lectures on Hitchin systems and their quantization given by the first author at the Beijing Summer Workshop in Mathematics and Mathematical Physics ``Integrable Systems…
Recently, Rogers' dilogarithm identities have attracted much attention in the setting of conformal field theory as well as lattice model calculations. One of the connecting threads is an identity of Richmond-Szekeres that appeared in the…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
Lecture notes from the Jerusalem Winter School on Theoretical Physics "Correlated Electron Systems", Dec. 1991 -- Jan. 1992. Contains a review of recent and not so recent results in the theory of correlated fermions in one dimension.
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
A quantum generalization of Rogers' five term, or ``pentagon'' dilogarithm identity is suggested. It is shown that the classical limit gives usual Rogers' identity. The case where the quantum identity is realized in finite dimensional space…
The status of the twist-2 and the twist-3 integral relations between polarized structure functions in deep inelastic scattering is discussed. The relations can be tested in the upcoming experiments in the range $Q^2 \gsim M_p^2$.
Two-loop Feynman integrals of the massive $\phi^4_d$ field theory are explicitly obtained for generic space dimensions $d$. Corresponding renormalization-group functions are expressed in a compact form in terms of Gauss hypergeometric…
In algebraic geometry, there is a reduction algorithm that transforms the unreduced divisor into a unique reduced divisor, which existence is guaranteed by the Riemann-Roch theorem. We discuss application of this algorithm to construction…
These are notes of lectures given at the Third School of Theoretical Physics in Jijel (Algeria, September 2009). The subject of these notes is differential geometry, complex and quaternionic structures with applications to theoretical…
We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…
A residue formula which evaluates any correlation function of topological $SU_n$ Yang-Mills theory with arbitrary magnetic flux insertion in two dimensions are obtained. Deformations of the system by two form operators are investigated in…
Topological bases of behaviour of trajectories for autonomous differential systems of the second order on sphere are stated. Stereographic atlas of trajectories is constructed. Differential connections between trajectories of…
We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…
We establish the regularity in 2 dimensions of $L^2$ solutions to critical elliptic systems in divergence form involving involution operators of finite $W^{1,2}$-energy.
I review recent progress in analysing deep inelastic scattering structure functions in global analyses. The new ingredients are new data and attempts to incorporate heavy quarks consistently. A new way of including the resummation of large…
Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
We review a recently-discovered link between the functional relations approach to integrable quantum field theories and the properties of certain ordinary differential equations in the complex domain.