Related papers: What are we quantizing in integrable field theory?
The subject of this paper is the consecutive procedure of discretization and quantization of two similar classical integrable systems in three-dimensional space-time: the standard three-wave equations and less known modified three-wave…
We use the ideas of symplectic quantization for quantizing fields in finite volumes. We consider, as examples, the Klein-Gordon and electromagnetic fields in three dif- ferent boxes. As a second idea we consider the given boundary…
We study different aspects of integrable boundary quantum field theories, focusing mostly on the ``boundary sine-Gordon model'' and its applications to condensed matter physics. The first part of the review deals with formal problems. We…
We show that the Ashtekar-Isham extension of the classical configuration space of Yang-Mills theories (i.e. the moduli space of connections) is (topologically and measure-theoretically) the projective limit of a family of finite dimensional…
By averaging over an ensemble of field configurations, a classical field theory can display many of the characteristics of quantum field theory, including Lorentz invariance, a loop expansion, and renormalization effects. There is…
Quantization relates Poisson algebras to $C^*$-algebras. The analysis of local gauge symmetries in algebraic quantum field theory is approached through the quantization of classical gauge theories, regarded as constrained dynamical systems.…
Certain phase space path integrals can be evaluated exactly using equivariant cohomology and localization in the canonical loop space. Here we extend this to a general class of models. We consider hamiltonians which are {\it a priori}…
We study the topology dependence of finite size corrections to the Ising model partition function by considering the model on a triangular lattice embedded on a genus two surface. At criticality we observe a universal shape dependent…
Every system in physics is described in terms of interacting elementary particles characterized by modulated spacetime recurrences. These intrinsic periodicities, implicit in undulatory mechanics, imply that every free particle is a…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
Path integral formulation of quantum mechanics defines the wavefunction associated with a particle as a sum of phase-factors, which are periodic functions of classical action. In the present article, this periodicity is shown to impart the…
Wigner's quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincar\'e group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase…
The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those which have, as their classical limit, a non-integrable classical system. In order to obtain this limit, the self-induced…
In this paper we study classical limit of conformal field theories realized by large N gauge theories using the generalized coherent states. For generic large N gauge theories with conformal symmetry, we show that the classical limit of…
Boundary conditions compatible with classical integrability are studied both directly, using an approach based on the explicit construction of conserved quantities, and indirectly by first developing a generalisation of the Lax pair idea.…
We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…
In quantum field theories, field redefinitions are often employed to remove redundant operators in the Lagrangian, making calculations simpler and physics more evident. This technique requires some care regarding, among other things, the…
The module category of any artin algebra is filtered by the powers of its radical, thus defining an associated graded category. As an extension of the degree of irreducible morphisms, this text introduces the degree of morphisms in the…
In this paper we relate a problem in representation theory - the study of Yetter-Drinfeld modules over certain braided Hopf algebras - to a problem in two-dimensional quantum field theory, namely the identification of integrable…
This article is a survey of classical and quantum completely integrable systems from the viewpoint of local ``phase space'' analysis. It advocates the use of normal forms and shows how to get global information from glueing local pieces.…