相关论文: Factorization and Topological States in $c=1$ Matt…
Factorization of the $N$-tachyon amplitudes in two-dimensional $c=1$ quantum gravity is studied by means of the operator product expansion of vertex operators after the Liouville zero mode integration. Short-distance singularities between…
We study the discrete state structure of $\hat c=1$ superconformal matter coupled to 2-D supergravity. Factorization properties of scattering amplitudes are used to identify these states and to construct the corresponding vertex operators.…
We consider the theory of pure gravity in 2+1 dimensions, with negative cosmological constant. The theory contains simple matter in the form of point particles; the later are classically described as lines of conical singularities. We…
The nonlinear structures in 2D quantum gravity coupled to the $(q+1,q)$ minimal model are studied in the Liouville theory to clarify the factorization and the physical states. It is confirmed that the dressed primary states outside the…
The two-dimensional (2-D) quantum gravity coupled to the conformal matter with $c=1$ is studied. We obtain all the three point couplings involving tachyons and/or discrete states via operator product expansion. We find that cocycle factors…
All the three point couplings involving tachyons and/or discrete states are obtained in $c=1$ two-dimensional (2-D) quantum gravity by means of the operator product expansion (OPE). Cocycle factors are found to be necessary in order to…
We study 3d quantum gravity with two asymptotically anti-de Sitter regions, in particular, using its relation with coupled Alekseev-Shatashvili theories and Liouville theory. Expressions for the Hartle-Hawking state, thermal $2n$-point…
We study point particles in 2+1 dimensional first order gravity using a triangulation to fix the connection and frame-field. The Hamiltonian is reduced to a boundary term which yields the total mass. The triangulation is dynamical with…
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 study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass…
A simple algebraic model for charged particle moving in two dimensional space under influence of singular magnetic field is given. The fundamental assumption for the model is that every charged particle coupled to the magnetic field is…
Two-dimensional matterless dilaton gravity is a topological theory and can be classically reduced to a (0+1)-dimensional theory with a finite number of degrees of freedom. If quantization is performed, a simple gauge invariant quantum…
The amplitude for emitting $n$ bosons factorizes into the product of $n$ single-boson emission amplitudes, if the source is energetic and abelian. If it is energetic but {\it non-abelian}, the amplitude is given by a sum of factorized {\it…
The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
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…
The study of factorization in the linearized gravity is extended to the graviton scattering processes with a massive scalar particle, with a massless vector boson and also with a graviton. Every transition amplitude is shown to be…
In this paper, I emphasize those features of the extended phase space approach to quantization of gravity that distinguish it among other approaches. First of all, it is the conjecture about non-trivial topology of the Universe which was…
We present a method for the first principles calculation of tachyon one-point amplitudes in $(2,2p+1)$ minimal Liouville gravity defined on a torus. The method is based on the higher equations of motion in the Liouville CFT. These equations…
We develop a new perspective on the discretization of the phase space structure of gravity in 2+1 dimensions as a piecewise-flat geometry in 2 spatial dimensions. Starting from a subdivision of the continuum geometric and phase space…