Conformal geometry of the supercotangent and spinor bundles

Michel, Jean-Philippe

doi:10.1007/s00220-012-1475-2

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Conformal geometry of the supercotangent and spinor bundles

Michel, Jean-Philippe

2012 • In Communications in Mathematical Physics, 312(2), p. 303-336

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https://hdl.handle.net/2268/160667

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10.1007/s00220-012-1475-2

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Keywords :

conformal geometry, symplectic supermanifold, spin geometry; geometric quantization; conformally invariant differential operators.

Abstract :

[en] We study the actions of local conformal vector fields X∈conf(M,g) on the spinor bundle of (M,g) and on its classical counterpart: the supercotangent bundle M of (M,g). We first deal with the classical framework and determine the Hamiltonian lift of conf(M,g) to M. We then perform the geometric quantization of the supercotangent bundle of (M,g), which constructs the spinor bundle as the quantum representation space. The Kosmann Lie derivative of spinors is btained by quantization of the comoment map. The quantum and classical actions of conf(M,g) turn, respectively, the space of differential operators acting on spinor densities and the space of their symbols into conf(M,g)-modules. They are filtered and admit a common associated graded module. In the conformally flat case, the latter helps us determine the conformal invariants of both conf(M,g)-modules, in particular the conformally odd powers of the Dirac operator.

Disciplines :

Mathematics

Author, co-author :

Michel, Jean-Philippe ; Université Claude Bernard - Lyon 1 - UCLB > Département de mathématique

Language :

English

Title :

Conformal geometry of the supercotangent and spinor bundles

Publication date :

2012

Journal title :

Communications in Mathematical Physics

ISSN :

0010-3616

eISSN :

1432-0916

Publisher :

Springer Science & Business Media B.V.

Volume :

312(2)

Pages :

303-336

Peer reviewed :

Peer Reviewed verified by ORBi

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since 06 January 2014

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