scholarly journals VACUUM ENERGY, SPECTRAL DETERMINANT AND HEAT KERNEL ASYMPTOTICS OF GRAPH LAPLACIANS WITH GENERAL VERTEX MATCHING CONDITIONS

2010 ◽  
Author(s):  
J. M. HARRISON ◽  
K. KIRSTEN
Keyword(s):  
Heat Kernel ◽  
Vacuum Energy ◽  
Matching Conditions ◽  
Graph Laplacians ◽  
Heat Kernel Asymptotics ◽  
Spectral Determinant

HEAT KERNEL ASYMPTOTICS FOR ROOTS OF GENERALIZED LAPLACIANS

2003 ◽  
Vol 14 (04) ◽  
pp. 397-412 ◽  
Author(s):  
CHRISTIAN BÄR ◽  
SERGIU MOROIANU
Keyword(s):  
Heat Kernel ◽  
Closed Manifold ◽  
Type Operator ◽  
Wodzicki Residue ◽  
Heat Trace ◽  
Heat Kernel Asymptotics ◽  
Laplace Type

We describe the heat kernel asymptotics for roots of a Laplace type operator Δ on a closed manifold. A previously known relation between the Wodzicki residue of Δ and heat trace asymptotics is shown to hold pointwise for the corresponding densities.

scholarly journals The Noncommutative Infinitesimal Equivariant Index Formula

2014 ◽  
Vol 14 (1) ◽  
pp. 73-102 ◽  
Author(s):  
Yong Wang
Keyword(s):  
Heat Kernel ◽  
Explicit Formula ◽  
Noncommutative Geometry ◽  
Index Formula ◽  
Equivariant Index ◽  
Heat Kernel Asymptotics

AbstractIn this paper, we establish an infinitesimal equivariant index formula in the noncommutative geometry framework using Greiner's approach to heat kernel asymptotics. An infinitesimal equivariant index formula for odd dimensional manifolds is also given. We define infinitesimal equivariant eta cochains, prove their regularity and give an explicit formula for them. We also establish an infinitesimal equivariant family index formula and introduce the infinitesimal equivariant eta forms as well as compare them with the equivariant eta forms.

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