Essays about: "Equivariant cohomology"

Found 3 essays containing the words Equivariant cohomology.

  1. 1. Supersymmetric Quantum Mechanics, Index Theorems and Equivariant Cohomology

    University essay from Uppsala universitet/Teoretisk fysik

    Author : Hans Nguyen; [2018]
    Keywords : supersymmetry; SUSY; quantum mechanics; index theorem; path integral; non-linear sigma model; spin complex; Chern-Gauss-Bonnet theorem; Witten index; equivariant cohomology; Weil model; Cartan model;

    Abstract : In this thesis, we investigate supersymmetric quantum mechanics (SUSYQM) and its relation to index theorems and equivariant cohomology. We define some basic constructions on super vector spaces in order to set the language for the rest of the thesis. READ MORE

  3. 2. Equivariant Localization in Supersymmetric Quantum Mechanics

    University essay from Uppsala universitet/Teoretisk fysik

    Author : Emil Hössjer; [2018]
    Keywords : Equivariant cohomology; localization; Cartan model; quantum mechanics; supersymmetry; partition function;

    Abstract : We review equivariant localization and through the Feynman formalism of quantum mechanics motivate its role as a tool for calculating partition functions. We also consider a specific supersymmetric theory of one boson and two fermions and conclude that by applying localization to its partition function we may arrive at a known result that has previously been derived using different approaches. READ MORE

  4. 3. Equivariant Cohomology and Localisation

    University essay from Uppsala universitet/Teoretisk fysik

    Author : Jaume Alonso i Fernández; [2015]
    Keywords : Equivariant Cohomology; localisation;

    Abstract : Equivariant localisation is based on exploiting certain symmetries of some systems, generally represented by a non-free action of a Lie group on a manifold, to reduce the dimensionality of integral calculations that commonly appear in theoretical physics. In this work we present Cartan's model of equivariant cohomology in different scenarios, such as differential manifolds, symplectic manifolds or vector bundles and we reproduce the main corresponding localisation results. READ MORE