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Related papers: Liouville field theory on a pseudosphere

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We establish Liouville type theorems in the whole space and in a half-space for parabolic problems without scale invariance. To this end, we employ two methods, respectively based on the corresponding elliptic Liouville type theorems and…

Analysis of PDEs · Mathematics 2024-10-01 Pavol Quittner , Philippe Souplet

We evaluate the three point function for arbitrary states in bosonic minimal models on the sphere coupled to quantum gravity in two dimensions. The validity of the formal continuation in the number of Liouville screening charge insertions…

High Energy Physics - Theory · Physics 2009-10-22 Kenichiro Aoki , Eric D'Hoker

This paper studies Liouville properties for viscosity sub- and supersolutions of fully nonlinear degenerate elliptic PDEs, under the main assumption that the operator has a family of generalized subunit vector fields that satisfy the…

Analysis of PDEs · Mathematics 2020-06-12 Martino Bardi , Alessandro Goffi

Elaborating on our previous presentation, where the term {\it dipolar quantization} was introduced, we argue here that adopting $L_0-(L_1+L_{-1})/2+{\bar L}_0-({\bar L}_1+{\bar L}_{-1})/2$ as the Hamiltonian instead of $L_0+{\bar L}_0$…

High Energy Physics - Theory · Physics 2016-11-18 Nobuyuki Ishibashi , Tsukasa Tada

We give applications of known and new Liouville type theorems to universal singularity and decay estimates for non scale invariant elliptic problems, including Lane-Emden and Schr\"odinger type systems. This applies to various classes of…

Analysis of PDEs · Mathematics 2025-04-30 Pavol Quittner , Philippe Souplet

Liouville theory describes the dynamics of surfaces with constant negative curvature and can be used to study the Weil-Petersson geometry of the moduli space of Riemann surfaces. This leads to an efficient algorithm to compute the…

High Energy Physics - Theory · Physics 2023-07-31 Sarah M. Harrison , Alexander Maloney , Tokiro Numasawa

The quantum-classical Liouville equation describes the dynamics of a quantum subsystem coupled to a classical environment. It has been simulated using various methods, notably, surface-hopping schemes. A representation of this equation in…

Other Condensed Matter · Physics 2010-11-17 Hyojoon Kim , Ali Nassimi , Raymond Kapral

In this thesis we study two-dimensional conformal field theories with Virasoro algebra symmetry, following the conformal bootstrap approach. Under the assumption that degenerate fields exist, we provide an extension of the analytic…

High Energy Physics - Theory · Physics 2019-02-06 Santiago Migliaccio

Lobachewsky geometry simulates a medium with special constitutive relations. The situation is specified in quasi-cartesian coordinates (x,y,z). Exact solutions of the Maxwell equations in complex 3-vector form, extended to curved space…

Mathematical Physics · Physics 2011-09-02 E. M. Ovsiyuk , V. M. Red'kov

The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize…

Mathematical Physics · Physics 2015-06-22 Decio Levi , Luigi Martina , Pavel Winternitz

We give a non-trivially interacting field theory example of scale invariant but non-conformal field theory. The model is based on the exactly solvable Liouville field theory coupled with free scalars deformed by an exactly marginal…

High Energy Physics - Theory · Physics 2014-11-18 Chiu Man Ho , Yu Nakayama

In this work, we construct a representation of the Virasoro algebra in the canonical Hilbert space associated to Liouville conformal field theory. The study of the Virasoro operators is performed through the introduction of a new family of…

Probability · Mathematics 2024-07-15 Guillaume Baverez , Colin Guillarmou , Antti Kupiainen , Rémi Rhodes , Vincent Vargas

In the present paper we derive Liouville type results and existence of periodic solutions for $\chi^{(2)}$ type systems with non-homogeneous nonlinearities. Moreover, we prove both universal bounds as well as singularity and decay estimates…

Analysis of PDEs · Mathematics 2023-06-27 Aleks Jevnikar , Jun Wang , Wen Yang

Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman…

General Relativity and Quantum Cosmology · Physics 2015-06-25 Hans-Thomas Elze

A four point function of basic Neveu-Schwarz exponential fields is constructed in the N = 1 supersymmetric Liouville field theory. Although the basic NS structure constants were known previously, we present a new derivation, based on a…

High Energy Physics - Theory · Physics 2008-11-26 A. Belavin , V. Belavin , A. Neveu , Al. Zamolodchikov

Two-dimensional conformal field theory is a powerful tool to understand the geometry of surfaces. Here, we study Liouville conformal field theory in the classical (large central charge) limit, where it encodes the geometry of the moduli…

High Energy Physics - Theory · Physics 2023-12-04 Kale Colville , Sarah M. Harrison , Alexander Maloney , Keivan Namjou

In this paper, exact one-point functions of N=1 super-Liouville field theory in two-dimensional space-time with appropriate boundary conditions are presented. Exact results are derived both for the theory defined on a pseudosphere with…

High Energy Physics - Theory · Physics 2015-06-26 Changrim Ahn , Chaiho Rim , Marian Stanishkov

An inverse scattering method based on an auxiliary inverse Sturm-Liouville problem recently proposed by Horv\'ath and Apagyi [Mod. Phys. Lett. B 22, 2137 (2008)] is examined in various aspects and developed further to (re)construct…

Mathematical Physics · Physics 2012-09-21 Tamas Palmai , Barnabas Apagyi

We argue that quantum Liouville field theory supplemented with a suitable source term is the effective theory which describes the short-range correlations of the gluon saturation momentum in the two-dimensional impact-parameter space, at…

High Energy Physics - Phenomenology · Physics 2008-11-26 Edmond Iancu , Larry McLerran

We consider the nonlinear equation $$-u'' = f(u) + h , \quad \text{on} \quad (-1,1),$$ where $f : {\mathbb R} \to {\mathbb R}$ and $h : [-1,1] \to {\mathbb R}$ are continuous, together with general Sturm-Liouville type, multi-point boundary…

Classical Analysis and ODEs · Mathematics 2015-09-22 Bryan P. Rynne