Communications in Mathematical Physics

, Volume 106, Issue 1, pp 159–176 | Cite as

The analysis of elliptic families. I. Metrics and connections on determinant bundles

  • Jean-Michel Bismut
  • Daniel S. Freed


In this paper, we construct the Quillen metric on the determinant bundle associated with a family of elliptic first order differential operators. We also introduce a unitary connection on λ and calculate its curvature. Our results will be applied to the case of Dirac operators in a forthcoming paper.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Differential Operator 
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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Jean-Michel Bismut
    • 1
  • Daniel S. Freed
    • 2
  1. 1.Départment de MathématiqueUniversité Paris-SudOrsayFrance
  2. 2.Department of MathematicsM.I.T.CambridgeUSA

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