相关论文: Quantum Trilogy: Discrete Toda, Y-System and Chaos

A scalar quantum field theory defined on a discrete spatial coordinate is examined. The renormalization of the lattice propagator is discussed with an emphasis on the periodic nature of the associated momentum coordinate. The analytic…

The 2-dimensional space-time sine-Gordon field theory is extended algebraically within the n-dimensional space of extended complex numbers. This field theory is constructed in terms of an adapted extension of standard vertex operators. A…

3D Loop Quantum Gravity with a vanishing cosmological constant can be related to the quantization of the $\textrm{SU}(2)$ BF theory discretized on a lattice. At the classical level, this discrete model characterizes discrete flat geometries…

The Toda lattice hierarchy is discussed in connection with the topological description of the $c=1$ string theory compactified at the self-dual radius. It is shown that when special constraints are imposed on the Toda hierarchy, it…

We study an integrable system related to the relativistic Toda lattice. The bilinear representation of this lattice is given and the B\"ackulund transformation obtained. A fully discrete version is also introduced with its bilinear…

A set of two-dimensional semi-riemannian submanifolds of flat semi-riemannian manifolds is associated to each Toda theory. The method and an example are given to Toda theories associated to real finite dimensional Lie algebras.

We study the quantization of the corner symmetry algebra of 3d gravity, that is the algebra of observables associated with 1d spatial boundaries. In the continuum field theory, at the classical level, this symmetry algebra is given by the…

Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed…

The direct linearisation framework is presented for the two-dimensional Toda equations associated with the infinite-dimensional Lie algebras $A_\infty$, $B_\infty$ and $C_\infty$, as well as the Kac--Moody algebras $A_{r}^{(1)}$,…

This paper investigates the relations between the Toda conformal field theories, quantum group theory and the quantisation of moduli spaces of flat connections. We use the free field representation of the $\mathcal{W}$-algebras to define…

We study the quantum Lyapunov exponent $\lambda_L$ in theories with spacetime-independent disorder. We first derive self-consistency equations for the two- and four-point functions for products of $N$ models coupled by disorder at large…

Many recent researches indicate that several gravitational D-dimensional theories suitably coupled to some matter fields (including in particular pure gravity in D dimensions, the low energy effective actions of the bosonic string and the…

We consider the two-dimensional $\mathfrak{sl}_n$ quantum Toda field theory with an imaginary background charge. This conformal field theory has a higher spin symmetry ($W_n$ algebra), a central charge $c \leq n-1$ and a continuous…

General properties of a class of two-dimensional dilaton gravity (DG) theories with multi-exponential potentials are studied and a subclass of these theories, in which the equations of motion reduce to Toda and Liouville equations, is…

We discuss a large class of classical field theories with continuous translation symmetry. In the quantum theory, a new anomaly explicitly breaks this translation symmetry to a discrete symmetry. Furthermore, this discrete translation…

We have recently proposed a simple relativistic theory which reduces to modified Newtonian dynamics for the weak-field quasistatic situations applied to galaxies, and to cosmological behavior as in the $\Lambda$CDM model, yielding a…

In this talk we describe our recent work on discrete quantum theory based on Galois fields. In particular, we discuss how discrete quantum theory sheds new light on the foundations of quantum theory and we review an explicit model of…

We apply the full theory of Loop Quantum Gravity (LQG) to cosmology and present a top-down derivation of gauge-invariant cosmological perturbation theory from quantum gravity. The derivation employs the reduced phase space formulation of…

We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…

We consider the application of the consistent lattice quantum gravity approach we introduced recently to the situation of a Friedmann cosmology and also to Bianchi cosmological models. This allows us to work out in detail the computations…