The Heat Kernel Method

Part of the Progress in Nonlinear Differential Equations and their Applications book series (PNLDE, volume 18)


The goal of the heat kernel method is to express (2.40) as an integral over the fixed point set Mγ in M of the transformation γ. Here Mγ = M if γ is the identity. The method is based on the following observations about arbitrary elliptic differential operators D, acting on sections of a smooth vector bundle F over a compact manifold M, which admits a a direct sum decomposition F = F+F-. In our case, F = EL, with the splitting F± = E±L, and D is the spin-c Dirac operator. For the required facts about trace class operators, see for instance Hörmander [42, Sec. 19.1], or Duistermaat [19].


Vector Bundle Integral Operator Heat Kernel Compact Manifold Integral Kernel 
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Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands

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