Related papers: Lectures on Polyfolds and Symplectic Field Theory
This paper studies how symplectic invariants created from Hamiltonian Floer theory change under the perturbations of symplectic structures, not necessarily in the same cohomology class. These symplectic invariants include spectral…
In this lecture note, we give a basic introduction to the rapidly developing concepts of generalized symmetries, from the perspectives of both high energy physics and condensed matter physics. In particular, we emphasize on the (invertible)…
In this paper we give a streamlined overview of some of the recent constructions provided with K.-H. Neeb, G. \'Olafsson and collaborators for a new geometric approach to Algebraic Quantum Field Theory (AQFT). Motivations, fundamental…
The purpose of this note is to make some connection between the sub-Riemannian geometry on Carnot-Caratheodory groups and symplectic geometry. We shall concentrate here on the Heisenberg group, although it is transparent that almost…
We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu-Schwarz and Ramond sectors of the orbifold theory as well as…
We propose a symplectic structure for the phase space of a generic Lagrangian field theory expressed in the framework of $L_\infty$ algebras. The symplectic structure does not require explicit knowledge of the derivative content of the…
We give a leisurely, albeit woefully incomplete, overview of quantum field theory, its relevance to condensed matter systems, and spin systems, which proceeds via a series of illustrative examples. The goal is to provide readers from the…
In this note I provide an extended version of the talk given at BW2011 workshop. The concise introduction to the non-local SFT motivated models is given with an emphasis on the non-local generalization of gravity. A number of open questions…
Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of…
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
Some early chapters of the upcoming book "Polyfold Constructions: Tools, Techniques, and Functors"
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…
The purpose of this mostly expository paper is to discuss a connection between Nielsen fixed point theory and symplectic Floer homology theory for symplectomorphisms of surface and a calculation of Seidel's symplectic Floer homology for…
These notes are an introduction to symplectic groupoids and the double structures associated with them. The treatment is intended to lie about midway between the original account of Coste, Dazord and Weinstein, which relied on effective use…
This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.
We construct symplectic submanifolds of symplectic manifolds with contact border. The boundary of such submanifolds is shown to be a contact submanifold of the contact border. We also give a topological characterization of the constructed…
The problem of reduction of multisymplectic manifolds by the action of Lie groups is stated and discussed, as a previous step to give a fully covariant scheme of reduction for classical field theories with symmetries.
The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and engineering. In this work, we study this manifold with the…
This document collects contributions to the Open Problem List in Billiards and Quantitative Symplectic Geometry, compiled following discussions during the workshop ``Billiards and quantitative symplectic geometry'' that took place at the…
This is a version of the author's diploma thesis written at the University of Cologne in 2002/03. The topic is the construction of Seiberg-Witten invariants of closed 3-manifolds. In analogy to the four dimensional case, the structure of…