Smooth Fock bundles, and spinor bundles on loop space

2020/09/01 by Peter Kristel, Kristel, Peter, Konrad Waldorf +1
Mathematics · Physics and Astronomy · #22E66 (Primary) #46N50 #53C27 #81R10 (Secondary) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2009.00333

openalex publication_date 2020/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We address the construction of smooth bundles of fermionic Fock spaces, a problem that appears frequently in fermionic gauge theories. Our main motivation is the spinor bundle on the free loop space of a string manifold, a structure anticipated by Killingback, with a construction outlined by Stolz-Teichner. We develop a general framework for constructing smooth Fock bundles, and obtain as an application a complete and well-founded construction of spinor bundles on loop space.

Citations

• Constructions with bundle gerbes
• Fundamentals of submersions and immersions between infinite-dimensional\n manifolds
• The Unitary Group In Its Strong Topology

Related

• The spinor bundle on loop space
• A bundle gerbe construction of a spinor bundle from the smooth free loop of a vector bundle
• The co-Riemannian Structure of Smooth Loop Spaces
• Fock bundles and Hitchin components
• The Geometry of the Loop Space and a Construction of a Dirac Operator