Natural bundles. II. Spin and the diffeomorphism group

DOI10.1063/1.530009zbMath0778.55008OpenAlexW2017992700MaRDI QIDQ3141378

S. Timothy Swift

Publication date: 6 January 1994

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530009

zbMATH Keywords

diffeomorphismsspinorsgeneral relativitymetricsfield theoriesgrand spin frame bundleinfinite dimensional spin structuremetric-spinor field configuration manifoldnatural infinite dimensional bundles

Mathematics Subject Classification ID

Applications of manifolds of mappings to the sciences (58D30) Applications of global differential geometry to the sciences (53C80) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15) Fiber spaces and bundles in algebraic topology (55R99)

Related Items

Eigenvalues of the Dirac operator on compact spin manifolds under Ricci flow ⋮ Resolution of simple singularities yielding particle symmetries in a space–time ⋮ Covariant spin structure ⋮ Nonlinear realizations of the diffeomorphism group in metric-affine gauge theory of gravity ⋮ Algebraic backgrounds for noncommutative Kaluza-Klein theory. I. Motivations and general framework ⋮ Background geometry in the gauge theory of gravity ⋮ Natural bundles. III. Resolving the singularities in the space of immersed submanifolds

Cites Work

• Gravitational anomalies and the family's index theorem
• Spinors and diffeomorphisms
• Determinants, torsion, and strings
• String structures on loop bundles
• Unitary representations of some infinite dimensional groups
• A relation between local and total energy in general relativity
• A new proof of the positive energy theorem.
• Momentum, angular momentum and their quasi-local null surface extensions
• Spinor structures on spheres and projective spaces
• Resolving the singularities in the space of Riemannian geometries
• Natural bundles. I. A minimal resolution of superspace