Related papers: The disk 1-point function in timelike Liouville th…
We compute N-point correlation functions of non-unitary (2k-1, 2) minimal matter coupled to 2D quantum gravity on a sphere using the continuum Liouville field approach. A gravitational dressing of the matter primary field with the minimum…
We construct the boundary ground ring in c < 1 open string theories with non-zero boundary cosmological constant (FZZT brane), using the Coulomb gas representation. The ring relations yield an over-determined set of functional recurrence…
Few years ago Zamolodchikov and Zamolodchikov proposed an expression for the 4-point classical Liouville action in terms of the 3-point actions and the classical conformal block. In this paper we develop a method of calculating the…
We give a recursive method to compute the classical conformal blocks in Liouville field theory. The values of the expansion coefficients are given by an algebraic scheme which works to all orders. The algebraic expression of the intervening…
In this paper we perform a blow-up and quantization analysis of the fractional Liouville equation in dimension $1$. More precisely, given a sequence $u_k :\mathbb{R} \to \mathbb{R}$ of solutions to \begin{equation} (-\Delta)^\frac{1}{2} u_k…
In this paper, we consider some blow-up problems for the 1D Euler equation with time and space dependent damping. We investigate sufficient conditions on initial data and the rate of spatial or time-like decay of the coefficient of damping…
This paper presents a systematic study for analytic aspects of discrete spectra methods for convolution of functions supported on disks, according to the Sturm-Liouville theory. We then investigate different aspects of the presented theory…
In this work we derive braid group representations and Stokes matrices for Liouville conformal blocks with one irregular operator. By employing the Coulomb gas formalism, the corresponding conformal blocks can be interpreted as…
A canonical quantization for two dimensional gravity models, including a dilaton gravity model, is performed in a way suitable for the light-cone gauge. We extend the theory developed by Abdalla {\it et.al.}\cite{AM} and obtain the…
We prove that the probabilistic definition of the most general boundary three-point and bulk-boundary structure constants in Liouville conformal field theory (LCFT) agree respectively with the formula proposed by Ponsot-Techsner (2002) and…
Correlation functions in Liouville theory are meromorphic functions of the Liouville momenta, as is shown explicitly by the DOZZ formula for the three-point function on the sphere. In a certain physical region, where a real classical…
Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions associated with the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type…
An exact mapping is established between the $c\geq25$ Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic confining potential. The probability distribution of…
Compared to the the classical first-order Gr\"unwald-Letnikov formula at time $t_{k+1} (\textmd{or}\, t_{k})$, we firstly propose a second-order numerical approximate scheme for discretizing the Riemann-Liouvile derivative at time…
A particle method for reproducing the phase space of collisionless stellar systems is described. The key idea originates in Liouville's theorem which states that the distribution function (DF) at time t can be derived from tracing necessary…
We study a relativistic quantum particle in cosmic string spacetime in the presence of a uniform magnetic field and a Coulomb-type scalar potential. It is shown that the radial part of this problem possesses the $su(1,1)$ symmetry. We…
We point out that there is a generalization to higher dimensions $d=2h>2$ of the two-dimensional Dotsenko-Fateev formula \DF\ for particular Coulomb gas conformal invariant integrals. These expressions represent structure constants of…
We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be reproduced using unitary…
Introducing an effective refraction index of an isotropic cosmic medium, we investigate the cosmological fluid dynamics which is consistent with a conformal, timelike symmetry of a corresponding ``optical'' metric. We demonstrate that this…
We determine the form factor expansion of the one-point functions in integrable quantum field theory at finite temperature and find that it is simpler than previously conjectured. We show that no singularities are left in the final…