Related papers: Elements of Geometric Quantization and Application…
Global Categorical Symmetries are a powerful new tool for analyzing quantum field theories. This volume compiles lecture notes from the 2022 and 2023 summer schools on Global Categorical Symmetries, held at the Perimeter Institute for…
These lectures present a brief introduction to measurement theory for QFT in possibly curved spacetimes introduced by the author and R. Verch [Comm. Math. Phys. 378 (2020) 851-889]. Topics include: a brief introduction to algebraic QFT,…
These are lecture notes of the QFT-I course I gave in an online mode at Chennai Mathematical Institute. The course focussed on the free relativistic quantum fields, their interactions in the perturbative scattering framework, standard…
The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses…
These are the notes from my courses on the arithmetic of quadratic forms.
These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…
These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications:…
The European School of High-Energy Physics is intended to give young physicists an introduction to the theoretical aspects of recent advances in elementary particle physics. These proceedings contain lecture notes on quantum field theory,…
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
Modern cosmology has created a tight link between particle physics / field theory and a wealth of new observational data on the structure of the Universe. These lecture notes focus on some of the most important aspects concerning the…
This is a paper compiled by students of the 2008 Summer School on Particles, Fields, and Strings held at the University of British Columbia on lectures given by Veronika Hubeny as understood and interpreted by the authors. We start with an…
Lecture notes prepared for the EMS--IAMP Spring School ``Symmetries and Measurement in Quantum Field Theory''. This set of lecture notes covers four lectures: 1. Operator Algebras and Quantum Field Theory, 2. Tomita-Takesaki Modular Theory…
This is a series of lecture notes explaining topos theory and its application in physics.
These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…
These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments discussed include new geometric features of…
These notes are an elaboration on: (i) a short course that I gave at the IPhT-Saclay in May-June 2012; (ii) a previous letter on reversibility in quantum mechanics. They present an introductory, but hopefully coherent, view of the main…
Lecture notes on selected topics in the theory of gravitation.
These notes are an introduction to General Relativity as a Quantum Effective Field Theory, following the material given in a short course on the subject at EPFL. The intent is to develop General Relativity starting from a quantum field…
These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The 4 topics covered are (1) Surface charges as conserved quantities in theories of gravity; (2) Classical…