Related papers: On the Exact Operator Formalism of Two-Dimensional…
Exact operator quantization is perfomed of a model of two-dimensional dilaton gravity in Lorentzian spacetime, classically equivalent to the one proposed by Callan, Giddings, Harvey and Strominger, in the special case with 24 massless…
The three-point functions for minimal models coupled to gravity are derived in the operator approach to Liouville theory which is based on its $U_q(sl(2))$ quantum group structure. The result is shown to agree with matrix-model calculations…
The Liouville action for two--dimensional quantum gravity coupled to interacting matter contains terms that have not been considered previously. They are crucial for understanding the renormalization group flow and can be observed in recent…
A recent study by Bojowald and Paily provided a path toward the identification of an effective quantum-spacetime picture of Loop Quantum Gravity, applicable in the "Minkowski regime", the regime where the large-scale (coarse-grained)…
This review contains a summary of work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables -the Liouville exponentials and the Liouville field itself -…
The purpose of this paper is to articulate a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space, based on the use of Kronecker product and what we have termed the `bra-flipper' operator.…
The Liouville approach is applied to the quantum treatment of the dilaton gravity in two dimensions. The physical states are obtained from the BRST cohomology and correlation functions are computed up to three-point functions. For the $N=0$…
We present an interesting reformulation of a collection of dilaton gravity models in two space-time dimensions into a field theory of two decoupled Liouville fields in flat space, in the presence of a Maxwell gauge field. An effective…
We construct the exponentials of the Liouville field with continuous powers within the operator approach. Their chiral decomposition is realized using the explicit Coulomb-gas operators we introduced earlier. {}From the quantum-group…
An infinite set of operator-valued relations in Liouville field theory is established. These relations are enumerated by a pair of positive integers $(m,n)$, the first $(1,1)$ representative being the usual Liouville equation of motion. The…
Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this…
Exact operator solution for quantum Liouville theory is investigated based on the canonical free field. Locality, the field equation and the canonical commutation relations are examined based on the exchange algebra hidden in the theory.…
This is the first part of an investigation concerning the formulation of 2D gravity in the framework of the uniformization theory of Riemann surfaces. As a first step in this direction we show that the classical Liouville action appears in…
If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using…
A large class of quantum field theories on 1+1 dimensional Minkowski space, namely, certain integrable models, has recently been constructed rigorously by Lechner. However, the construction is very abstract and the concrete form of local…
We present a family of classical spacetimes in 2+1 dimensions. Such a spacetime is produced by a Nambu-Goto self-gravitating string. Due to the special properties of three-dimensional gravity, the metric is completely described as a…
We study quantisation of noncommutative gravity theories in two dimensions (with noncommutativity defined by the Moyal star product). We show that in the case of noncommutative Jackiw-Teitelboim gravity the path integral over gravitational…
We derive a manifestly duality-symmetric formulation of the action principle for conformal gravity linearized around Minkowski space-time. The analysis is performed in the Hamiltonian formulation, the fourth-order character of the equations…
The continuum (Liouville) approach to the two-dimensional (2-D) quantum gravity is reviewed with particular attention to the $c=1$ conformal matter coupling, and new results on a related problem of dilaton gravity are reported. After…
We try to develop a coherent picture on Liouville theory as a two-dimensional conformal field theory that takes into account the perspectives of path-integral approach, bootstrap, canonical quantization and operator approach. To do this, we…