The Holst Action by the Spectral Action Principle

We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields.

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Veröffentlicht in:	Communications in mathematical physics 2011-10, Vol.307 (1), p.261-273
Hauptverfasser:	Pfäffle, Frank, Stephan, Christoph A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Classical and Quantum Gravitation Complex Systems Exact sciences and technology Linear and multilinear algebra, matrix theory Manifolds and cell complexes Mathematical analysis Mathematical and Computational Physics Mathematical methods in physics Mathematical Physics Mathematics Ordinary differential equations Other topics in mathematical methods in physics Physics Physics and Astronomy Quantum Physics Relativity Theory Sciences and techniques of general use Theoretical Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Beschreibung
Zusammenfassung:	We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields.
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-011-1303-0