Physics – Mathematical Physics
Scientific paper
2008-10-27
Commun.Math.Phys.291:543-577,2009
Physics
Mathematical Physics
LaTeX, 45 pages, in version 2 a typo has been corrected
Scientific paper
10.1007/s00220-009-0804-6
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 $G\times U(1)$ 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 $M\times M$ 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.
Avramidi Ivan G.
Fucci Guglielmo
No associations
LandOfFree
Non-perturbative Heat Kernel Asymptotics on Homogeneous Abelian Bundles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Non-perturbative Heat Kernel Asymptotics on Homogeneous Abelian Bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-perturbative Heat Kernel Asymptotics on Homogeneous Abelian Bundles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-324633