Quantization of Hamiltonian loop group spaces

DOI10.1007/s00208-018-1771-zzbMath1416.81068arXiv1804.00110OpenAlexW2895194414MaRDI QIDQ2423427

Yanyan Li

Publication date: 21 June 2019

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.00110

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Loop groups and related constructions, group-theoretic treatment (22E67) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Infinite loop spaces (55P47) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (6)

Geometric \(K\)-homology and the Freed-Hopkins-Teleman theorem ⋮ Deformation of Dirac operators along orbits and quantization of noncompact Hamiltonian torus manifolds ⋮ Quantization of Hamiltonian loop group spaces ⋮ A \(KK\)-theoretic perspective on deformed Dirac operators ⋮ Towards a quantization of the double via the enhanced symplectic ``category ⋮ Norm-square localization and the quantization of Hamiltonian loop group spaces

Cites Work

• Dirac operators on quasi-Hamiltonian \(G\)-spaces
• Norm-square localization for Hamiltonian \(L G\)-spaces
• Loop groups and twisted \(K\)-theory. III
• The \(KK\)-product of unbounded modules
• Equivariant KK-theory and the Novikov conjecture
• An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg
• Geometric quantization and multiplicities of group representations
• Schrödinger and Dirac operators with singular potentials and hyperbolic equations
• Symplectic surgery and the Spin\(^c\)-Dirac operator
• Lie group valued moment maps
• Proper group actions and the Baum-Connes conjecture
• Equivariant Dirac operators and differentiable geometric invariant theory
• Hamiltonian loop group actions and Verlinde factorization
• Index theorem for equivariant Dirac operators on noncompact manifolds
• The Verlinde formulas as fixed point formulas.
• Surjectivity for Hamiltonian loop group spaces
• A \(K\)-theoretic relative index theorem and Callias-type Dirac operators
• Geometric \(K\)-homology and the Freed-Hopkins-Teleman theorem
• \(LT\)-equivariant index from the viewpoint of \(KK\)-theory. A global analysis on the infinite-dimensional Heisenberg group
• Spinor modules for Hamiltonian loop group spaces
• An analytic \(LT\)-equivariant index and noncommutative geometry
• Quantization of Hamiltonian loop group spaces
• Essential self-adjointness of powers of generators of hyperbolic equations
• Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
• Equivariant indices of \(\operatorname{Spin}^c\)-Dirac operators for proper moment maps
• A short proof of an index theorem
• Dirac Structures and Dixmier–Douady Bundles
• Twisted K-Homology and Group-Valued Moment Maps
• Loop groups and twisted $K$-theory II
• Witten Non Abelian Localization for Equivariant K-Theory, and the [𝑄,𝑅=0 Theorem]
• Guide to Elliptic Boundary Value Problems for Dirac-Type Operators
• Exactness and the Kadison-Kaplansky conjecture
• Localization of the Riemann-Roch character
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Quantization of Hamiltonian loop group spaces