Hilbert Space of Spinor Fields Over the Free Loop Space

DOI10.1142/S0129055X97000099zbMath1004.58503OpenAlexW2013605555MaRDI QIDQ3130096

Rémi Léandre

Publication date: 16 February 2003

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

Full work available at URL: https://doi.org/10.1142/s0129055x97000099

zbMATH Keywords

Dirac operatorloop spaceHilbert space of continuous spinors

Mathematics Subject Classification ID

Spin and Spin({}^c) geometry (53C27) Group structures and generalizations on infinite-dimensional manifolds (58B25)

Related Items (4)

STOCHASTIC PROCESSES ON CLASSIFYING SPACES AND STRING STRUCTURES ⋮ Quotient of a loop group and Witten genus ⋮ String structure over the Brownian bridge ⋮ Stochastic Cohomology of the Frame Bundle of the Loop Space

Cites Work

• Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces
• Differential forms on loop spaces and the cyclic bar complex
• String structures and the path fibration of a group
• Exponential decay of the heat kernel over the diagonal. II
• Orientation and string structures on loop space
• String structures on loop bundles
• Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory
• Logarithmic Sobolev inequalities on loop groups
• Integration on loop groups. III: Asymptotic Peter-Weyl orthogonality
• A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
• Path integral formulae for heat kernels and their derivatives
• The geometry of degree-four characteristic classes and of line bundles on loop spaces. I
• \(S^ 1\)-actions and elliptic genera
• Characteristic forms and geometric invariants
• A stochastic approach to the Euler-Poincaré number of the loop space of a developable orbifold
• Hypoelliptic second order differential equations
• Potential theory on Hilbert space
• Iterated integrals of differential forms and loop space homology
• Pfaffians on Hilbert space
• Transformations of the Brownian motion on a Riemannian symmetric space
• [https://portal.mardi4nfdi.de/wiki/Publication:3889862 Martingales, the Malliavin calculus and hypoellipticity under general H�rmander's conditions]

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