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Article overview
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Non-perturbative Heat Kernel Asymptotics on Homogeneous Abelian Bundles | | Ivan G. Avramidi
; Guglielmo Fucci
; | | Date: |
27 Oct 2008 | | Abstract: | We study the heat kernel for a Laplace type partial differential operator
acting on smooth sections of a complex vector bundle with the structure group
$G imes U(1)$ over a Riemannian manifold $M$ without boundary. The total
connection on the vector bundle naturally splits into a $G$-connection and a
U(1)-connection, which is assumed to have a parallel curvature $F$. We find a
new local short time asymptotic expansion of the off-diagonal heat kernel
$U(t|x,x’)$ close to the diagonal of $M imes M$ assuming the curvature $F$ to
be of order $t^{-1}$. The coefficients of this expansion are polynomial
functions in the Riemann curvature tensor (and the curvature of the
$G$-connection) and its derivatives with universal coefficients depending in a
non-polynomial but analytic way on the curvature $F$, more precisely, on $tF$.
These functions generate all terms quadratic and linear in the Riemann
curvature and of arbitrary order in $F$ in the usual heat kernel coefficients.
In that sense, we effectively sum up the usual short time heat kernel
asymptotic expansion to all orders of the curvature $F$. We compute the first
three coefficients (both diagonal and off-diagonal) of this new asymptotic
expansion. | | Source: | arXiv, 0810.4889 | | Services: | Forum | Review | PDF | Favorites | |
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