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

By L. Faddeev, R. Kashaev, A. Volkov. 2000

250 citations recorded by the source corpus.

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 Hermitian conjugation, satisfying two discrete quantum Liouville equations, and living in mutually commuting subalgebras of the quantum algebra of observables.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5453bdb81ca443a925dd7be60d247af84016b142

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Quantum Riemann Surfaces in Chern-Simons Theory (2011, background): “nd q := e~~ ; (6.13) or via an integral formula ~=2 = exp 1 4 Z R+i dx x e ipx sinh(ˇx)sinh(~x=(2i)) : (6.14) Properties of this remarkable function have been discussed in many places, including [75, 19, 76, 77, 78, 79, 80, 2]. It was central to the state integral model constructed by [2, 20, 73].”
Dilaton gravity in two-dimensions (2002, background): “Recently again interesting developments should be noted in Liouville gravity [151, 406].”
Exact results for perturbative Chern-Simons theory with complex gauge group. (2009, unknown): “ the analysis, so we will describe the main properties of all three here. We give complete proofs, but only sketchily since none of this material is new. For further discussion and proofs, see, e.g., [13, 14, 15, 51, 20], and [57] (subsection II.1.D). 1. The asymptotic formula (3.18) can be reﬁned t”
The quantum dilogarithm and representations of quantum cluster varieties (2007, methodology): “The quantum pentagon relation for the function � ~ (z) was suggested in [Fad] and proved in different ways/forms in [Wo],[ FKV ] and [Go2].”
Generalized volume conjecture and the A-polynomials: The Neumann–Zagier potential function as a classical limit of the partition function (2006, methodology): “We note that the Fourier transformation of the Faddeev integ ral can be computed as follows [5, 14,31,54]; 1”
Essays on the theory of elliptic hypergeometric functions (2008, background): “1 References 58”