# Quantum Completely Integrable Models in Field Theory

@inproceedings{Faddeev1995QuantumCI,
title={Quantum Completely Integrable Models in Field Theory},
year={1995}
}
162 Citations
Fock representations of ZF algebras and R-matrices
• Art
Letters in Mathematical Physics
• 2020
<jats:p> A variation of the Zamolodchikov–Faddeev algebra over a finite-dimensional Hilbert space <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathcal {H}}$$</jats:tex-math><mml:math
The Q-Operator for the Quantum NLS Model
• Physics
Journal of Mathematical Sciences
• 2019
In this paper we show that the operator introduced by A. A. Tsvetkov enjoys all the needed properties of a Q-operator. It is shown that the Q-operator of the XXX spin chain with generic values of
Bethe ansatz solution of a nonlinear quantum field model in quasi-two dimensions linked to the Landau – Lifshitz equation
Integrable quantum field models are known to exist mostly in one space-dimension. Exploiting the concept of multi-time in integrable systems and a Lax matrix of higher scaling order, we construct a
Unraveling hidden hierarchies and dual structures in an integrable field model
An integrable field theory, due to path-independence on the space-time plane, should yield together with an infinite set of independent conserved charges also similar dual charges determining the
Q A ] 2 8 M ar 2 00 4 ITEP-TH1 / 04 Representation theory and quantum integrability ∗
• Mathematics
• 2004
We describe new constructions of the infinite-dimensional representations of U(g) and Uq(g) for g being gl(N) and sl(N). The application of these constructions to the quantum integrable theories of
Ju l 2 01 1 Yangians , S-matrices and AdS / CFT
This review is meant to be an account of the properties of the i nfinitedimensional quantum group (specifically, Yangian) symmetr y lying behind the integrability of the AdS/CFT spectral problem. In
Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology
• Physics
• 2010
In the present work we review the twisted field construction of quantum field theory on noncommutative spacetimes based on twisted Poincare invariance. We present the latest development in the field,
Determinantal Representation of the Time-Dependent Stationary Correlation Function for the Totally Asymmetric Simple Exclusion Model ?
The basic model of the non-equilibrium low dimensional physics the so-called totally asymmetric exclusion process is related to the 'crystalline limit' (q ! 1) of the SUq(2) quantum algebra. Using
The One-Dimensional Hubbard Model: Index
• Physics
• 2005
The description of a solid at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons. It is impossible to solve the corresponding