  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.
