Related papers: Elements of Geometric Quantization and Application…
These are notes of lectures given at the Third School of Theoretical Physics in Jijel (Algeria, September 2009). The subject of these notes is differential geometry, complex and quaternionic structures with applications to theoretical…
This lecture reviews aspects of and prospects for progress towards a theory of quantum gravity from a particle physics perspective, also paying attention to recent findings of the LHC experiments at CERN.
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.
We discuss recent developments in the hydrodynamic description of strongly coupled conformal field theories using the AdS/CFT correspondence. In particular, we review aspects of the fluid-gravity correspondence which provides a map between…
These lectures are an introduction to formal semiclassical quantization of classical field theory. First we develop the Hamiltonian formalism for classical field theories on space time with boundary. It does not have to be a cylinder as in…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
In this thesis we investigate topological aspects and arithmetic structures in quantum field theory and string theory. Particular focus is put on consistent truncations of supergravity and compactifications of F-theory.
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…
Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical…
The purpose of these lectures is to discuss in some detail a new, non-perturbative approach to quantum gravity. I would like to present the basic ideas, outline the key results that have been obtained so far and indicate where we are headed…
A geometric interpretation of quantum self-interacting string field theory is given. Relations between various approaches to the second quantization of an interacting string are described in terms of the geometric quantization. An algorithm…
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution…
These lecture notes in geometric mechanics are meant to convey insight through clear definitions and workable examples. The lecture format adopted here is intended to convey the immediacy of the taught course and to be useful as a basis for…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
These notes are a record of lectures given in the Workshop on Connections Between Algebra and Geometry at the University of Regina, May 29--June 1, 2012. The lectures were meant as an introduction to current research problems related to fat…
The paper is devoted to a description of quantum group structures in the geometric quantization of a self-interacting string field, which appear under a transition from a tree-level of the theory to the account of loop effects in…
These are notes from talks given at a spring school on topological quantum field theory in Nova Scotia during May of 2023. The aim is to introduce the reader to the role of factorization algebras and related concepts in field theory. In…
These lecture notes formed the basis of a mini-course on algebraic quantum field theory presented at the Bootstrap 2024 conference in Madrid. The goal of the notes is to explain the merits of algebraic quantum field theory to a broad…