Related papers: Loop Quantum Geometry: A primer
This article is an extended version of the peer-reviewed publication; Moffat and Wang, J Phys Math 2018, 9:4 DOI: 10.4172/2090-0902.1000289 The article sets out to address a number of issues concerning Loop Quantum Gravity raised by…
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
In these lectures several aspects of anyon in one and two dimensions are considered from the path integral formalism. This paper is based in a set of four lectures given by the author in the "V Latinoamerican Workshop of Particles and…
We present a pedagogical introduction to SU(2) recoupling theory, focusing on those aspects of the topic which are useful for practical calculations in loop quantum gravity. In particular, we give a self-contained presentation of the…
These are notes from a 15 week course aimed at graduate mathematicians. They provide an essentially self-contained introduction to some of the ideas and terminology of QFT.
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
The AdS/CFT correspondence provides quantum theories of gravity in which spacetime and gravitational physics emerge from ordinary non-gravitational quantum systems with many degrees of freedom. Recent work in this context has uncovered…
These are lecture notes of a mini-course given by the first author in Moscow in July 2019, taken by the second author and then edited and expanded by the first author. They were also a basis of the lectures given by the first author at the…
Lectures given at International School of Physics ``Enrico Fermi'', Varenna, Villa Monastero, June 28-July 7 1994
The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some…
In recent years, Loop Quantum Gravity has emerged as a solid candidate for a nonperturbative quantum theory of General Relativity. It is a background independent theory based on a description of the gravitational field in terms of…
Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
We study the euclidean covariant loop-quantum-gravity vertex numerically, using a cylindrically symmetric boundary state and a convenient value of the Barbero-Immirzi parameter. We show that a classical geometry emerges already at low spin.…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.
The exploration of the Riemannian structure of the Hilbert space has led to the concept of quantum geometry, comprising geometric quantities exemplified by Berry curvature and quantum metric. While this framework has profoundly advanced the…
In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While researchers are still facing the challenge of observing quantum gravity, there is a geometrical core to loop quantum gravity that does much to…
A program was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and their solutions through a toy model: quantum…