Related papers: Elements of Geometric Quantization and Application…
Condensed account of the Lectures delivered at the Meeting on {\it Noncommutative Geometry in Field and String Theory}, Corfu, September 18 - 20, 2005.
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
These are notes of lectures on spinning particles and the worldline formalism originally given by Olindo Corradini and Christian Schubert at the School on Spinning Particles in Quantum Field Theory: Worldline Formalism, Higher Spins, and…
This paper records my opening remarks at Nobel Symposium 148, on Graphene and Quantum Matter, at Saltsj\"obaden, Sweden, in June 2010. After some broad comments on the quantum theory of matter as a frontier of physics, and some slightly…
This is a brief reminder, with extensions, from a different angle and for a less specialized audience, of my presentation at WGMP32 in July 2013, to which I refer for more details on the topics hinted at in the title, mainly deformation…
These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
These notes are an expanded version of lectures given at the Croatian School on Black Holes at Trpanj, June 21-25, 2010. The aim is to provide a practical introduction to quantum field theory in curved spacetime and related black hole…
These are notes from my lectures at TASI 2015. The goal is to provide context for the study of strongly-correlated quantum many-body systems using quantum field theory, and possibly string theory.
After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a…
Lecture notes from the 2017 Les Houches Summer School on Effective Field Theories. The lectures covered introductory material on EFTs as used in high energy physics to compute experimentally observable quantities. Other lectures at the…
The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the…
The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
These lecture notes provide a relatively self-contained introduction to field theoretic methods employed in the study of classical and quantum phase transitions.
This survey article is an invited contribution to the Encyclopedia of Mathematical Physics, 2nd edition. We provide an accessible overview on relevant applications of higher and derived geometry to theoretical physics, including higher…
These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students,…
In this pedagogical introduction, I discuss theoretical aspects of superfluidity and superconductivity, mostly using a field-theoretical formalism. While the emphasis is on general concepts and mechanisms behind superfluidity, I also…
These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and…