Related papers: Lectures on classical Affine Gaudin models
We introduce the concept of multisymplectic formalism, familiar in covariant field theory, for the study of integrable defects in 1+1 classical field theory. The main idea is the coexistence of two Poisson brackets, one for each spacetime…
In this paper, we present a general scheme to construct integrable systems based on realization in the coboundary dynamical Poisson groupoids of Etingof and Varchenko. We also present a factorization method for solving the Hamiltonian…
We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} Hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the generalized…
Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural…
We propose a general method for constructing boundary integrable Gaudin models associated with (twisted) affine algebras ${\cal G}^{(k)} (k=1, 2)$, where ${\cal G}$ is a simple Lie algebra or superalgebra. Many new integrable Gaudin models…
The semiclassical limit of full non-commutative gauge theory is known as Poisson gauge theory. In this work we revise the construction of Poisson gauge theory paying attention to the geometric meaning of the structures involved and advance…
Since the work of Henri Cartan finite dimensional Riemannian symmetric spaces are an important subject of mathematical interest. They are related in a natural way to semisimple Lie groups. In this work we introduce and study their infinite…
Motivated by the notion of Lagrangian multiforms, which provide a Lagrangian formulation of integrability, and by results of the authors on the role of covariant Hamiltonian formalism for integrable field theories, we propose the notion of…
We investigate an effective Hamiltonian for QCD at large s, in which longitudinal gauge degrees of freedom are suppressed, but not eliminated. In an axial gauge the effective field theory is a set of coupled (1+1)-dimensional…
Canonical structure of the space-time symmetric analogue of the Hamiltonian formalism in field theory based on the De Donder-Weyl (DW) theory is studied. In $n$ space-time dimensions the set of $n$ polymomenta is associated to the…
We introduce a generalized Gaudin Lie algebra and a complete set of mutually commuting quantum invariants allowing the derivation of several families of exactly solvable Hamiltonians. Different Hamiltonians correspond to different…
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong…
The objective of the present work -- a literature review on both gapped and gapless fractonic theories -- is to pedagogically fill in the gaps between the research on fractons, and an undergraduate physics education (particularly quantum…
The closed string model in the background gravity field is considered as the bi-Hamiltonian system in assumption that string model is the integrable model for particular kind of the background fields. The dual nonlocal Poisson brackets, de…
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
Local higher-spin conserved currents are constructed in the supersymmetric sigma models with target manifolds symmetric spaces $G/H$. One class of currents is based on generators of the de Rham cohomology ring of $G/H$; a second class of…
We bring together aspects of covariant Hamiltonian field theory and of classical integrable field theories in $1+1$ dimensions. Specifically, our main result is to obtain for the first time the classical $r$-matrix structure within a…
These are expanded and revised notes for a minicourse entitled "Affine W-algebras", which took place as part of the thematic month "Quantum Symmetries" at the Centre de Recherches Mathematiques in Montreal, Canada in October 2022. The first…
We determine the quantized function algebras associated with various examples of generalized sine-Gordon models. These are quadratic algebras of the general Freidel-Maillet type, the classical limits of which reproduce the lattice Poisson…
These lecture notes provide a pedagogical introduction, with exercises, to the techniques used in attempts to construct vacua with stabilised moduli in string theory. The reader is only assumed to have a basic knowledge of general…