These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism.
Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory
These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to convergence that are typically taught in the first or second year of undergraduate studies, no other background is needed to read the notes. The notes might be also of interest to any mathematically inclined reader who wishes to learn basic facts about notions of entropy in an elementary setting.
Lecture notes to a one-term course on operator algebras and their application in physics. Very brief and basic introduction to the subject of Banach- and C-star algebras complemented with their appearance in physics. The course is intended at mathematics students in their master program with a basic knowledge of functional analysis and some interest in the foundations of quantum mechanics.
The goal of these lectures is to exhibit the framing anomaly in the Batalin-Vilkovisky formulation of perturbative Chern-Simons theory. Concretely, we show that the partition function fails to satisfy the Quantum Master Equation, and show that this can be remedied at the cost of introducing a framing. Along the way, we discuss principal bundles and connections, the Chern-Simons action functional, and perturbative quantization of gauge theories in the Batalin-Vilkovisky formalism.
This lecture note surveys the gamma matrices in general dimensions with arbitrary signatures, the study of which is essential to understand the supersymmetry in the corresponding spacetime. The contents supplement the lecture presented by the author at Modave Summer School in Mathematical Physics, Belgium, June, 2005.
These lecture notes accompanied the course Time-Frequency Analysis given at the Faculty of Mathematics of the University of Vienna in the summer term 2021. The material is suitable for an advanced undergraduate course in mathematics or a mathematics class for PhD students. Besides standard linear algebra and calculus only some basics from functional analysis are needed. A course in Fourier analysis may be of advantage, but is not needed. The course contained 4 academic units per week. The appendices and Section 11 were not presented in class.
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 scattering amplitudes, for instance, integrand reduction, residue computation in unitarity analysis and Integration-by-parts reduction. Illustrative examples and exercises are included in these notes.
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics. The main objective of these notes is to introduce a student who is familiar with concepts in linear algebra and partial differential equations to select topics in deep learning. These lecture notes exploit the strong connections between deep learning algorithms and the more conventional techniques of computational physics to achieve two goals. First, they us…
These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo Institute of Technology, October 2019. I overview in a pedagogical fashion the main aspects of the theory of generalised hydrodynamics, a hydrodynamic theory for quantum and classical many-body integrable systems. Only very basic knowledge of hydrodynamics and integrable systems is assumed.
