相关论文: Introduction to the Liouville quantum gravity metr…
The quantum Liouville equation, which describes the phase space dynamics of a quantum system of fermions, is analyzed from statistical point of view as a particular example of the Kramers-Moyal expansion. Quantum mechanics is extended to…
Content: 1. Introduction 2. Regge calculus and dynamical triangulations Simplicial manifolds and piecewise linear spaces - dual complex and volume elements - curvature and Regge action - topological invariants - quantum Regge calculus -…
Loop Quantum Gravity (L.Q.G.) is one of the two most promising tentative theory for a quantum description of gravity. When applied to the entire universe, the so-called Loop Quantum Cosmology (L.Q.C.) framework offers microscopical models…
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…
Following de Broglie and Vigier, a fully relativistic causal interpretation of quantum mechanics is given within the context of a geometric theory of gravitation and electromagnetism. While the geometric model shares the essential…
The efforts in this contribution consist in reassessing a modified Dirac equation that incorporates a $\gamma^0 \gamma_5$-Lorentz-symmetry violating (LSV) term induced as a Loop Quantum Gravity (LQG) effect. Originally, this equation has…
Getting signatures of quantum gravity is one of the topical lines of research in modern theoretical physics and cosmology. This short review faces this challenge under a novel perspective. Instead of separating quantum-gravity effects of a…
An Ansatz for the Poincar\'e metric on compact Riemann surfaces is proposed. This implies that the Liouville equation reduces to an equation resembling a non chiral analogous of the higher genus relationships (KP equation) arising in the…
Canonical quantum gravity was first developed by Abhay Ashtekar, Lee Smolin, Carlo Rovelli and their collaborators in the late 1980s. It was a major breakthrough that successfully brought Einstein's theory of General Relativity (GR) into a…
We calculate a class of two-point boundary correlators in 2D quantum gravity using its microscopic realization as loop gas on a random surface. We find a perfect agreement with the two-point boundary correlation function in Liouville…
The first chapters introduce briefly conformal theories, Moore and Seiberg polynomial equations and Gervais-Neveu quantization of Liouville theory. The next chapters present the original results of this thesis. First, the algebra of the…
The most important problem of fundamental Physics is the quantization of the gravitational field. A main difficulty is the lack of available experimental tests that discriminate among the theories proposed to quantize gravity. Recently we…
Differential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantum gauge theory of gravity which is proposed in the references hep-th/0109145 and hep-th/0112062 is formulated completely in the…
We study the Klein-Gordon equation in one spatial and one temporal dimension. Physically, this equation describes the wave function of a relativistic spinless boson with positive rest mass. Mathematically, this is the most elementary…
The aim of this dissertation is to review `Loop Quantum Gravity', explaining the main structure of the theory and indicating its main open issues. We will develop the two main lines of research for the theory: the canonical quantization…
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental…
The purpose of these notes, based on a course given by the second author at Les Houches summer school, is to explain the probabilistic construction of Polyakov's Liouville quantum gravity using the theory of Gaussian multiplicative chaos.…
This work is devoted to the analysis of the quantum Liouville-BGK equation. This equation arises in the work of Degond and Ringhofer on the derivation of quantum hydrodynamical models from first principles. Their theory consists in…
Can you hear the shape of Liouville quantum gravity? We obtain a Weyl law for the eigenvalues of Liouville Brownian motion: the $n$-th eigenvalue grows linearly with $n$, with the proportionality constant given by the Liouville area of the…
At the beginning of the previous century, Newtonian mechanics fell victim to two new revolutionary theories, Quantum Mechanics (QM) and General Relativity (GR). Both theories have transformed our view of physical phenomena, with QM…