Strongly Coupled Quantum Discrete Liouville Theory.¶I: Algebraic Approach and Duality

2000/06/20 by L. D. Faddeev, Rinat Kashaev, R. M. Kashaev +1 · 209 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Duality (order theory) #Exponential function #Hermitian matrix #Hilbert space #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Observable #Operator (biology) #Physics #Pure mathematics #Quantum #Quantum chaos and dynamical systems #Quantum many-body systems #Quantum mechanics #Self-adjoint operator #Unitary state #hep-th

paper · pdf · doi:10.1007/s002200100412

published in Communications in Mathematical Physics 219(1), 199-219 (Springer Science+Business Media) · Latex2e, 20 pages

arxiv created 2000/06/20 · openalex publication_date 2001/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The quantum discrete Liouville model in the strongly coupled regime, 1<c<25, is formulated as a well defined quantum mechanical problem with unitary evolution operator. The theory is self-dual: there are two exponential fields related by Hermitean conjugation, satisfying two discrete quantum Liouville equations, and living in mutually commuting subalgebras of the quantum algebra of observables.

Citations

• Algebraic Quantization of Integrable Models in Discrete Space-time
• Infinite conformal symmetry in two-dimensional quantum field theory
• Quantum geometry of bosonic strings
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• How Algebraic Bethe Ansatz works for integrable model
• Liouville central charge in quantum Teichmuller theory

Cited by

• Continuum Limit of the Volterra Model, Separation of Variables and Non-Standard Realizations of the Virasoro Poisson Bracket
• Unit Circle Elliptic Beta Integrals
• Baxter Q-operators and representations of Yangians
• The quantum dilogarithm and representations of quantum cluster varieties