scholarly journals Differential forms and the Wodzicki residue for manifolds with boundary

2006 ◽  
Vol 56 (5) ◽  
pp. 731-753 ◽  
Author(s):  
Yong Wang
Keyword(s):  
Differential Forms ◽  
Manifolds With Boundary ◽  
Wodzicki Residue

scholarly journals Differential forms on manifolds with boundary and corners

2019 ◽  
Vol 30 (5) ◽  
pp. 920-929
Author(s):  
Serap Gürer ◽  
Patrick Iglesias-Zemmour
Keyword(s):  
Differential Forms ◽  
Manifolds With Boundary

scholarly journals A Kastler–Kalau–Walze type theorem for five-dimensional manifolds with boundary

2015 ◽  
Vol 12 (05) ◽  
pp. 1550064 ◽  
Author(s):  
Jian Wang ◽  
Yong Wang
Keyword(s):  
General Relativity ◽  
Dirac Operator ◽  
Type Theorem ◽  
Manifolds With Boundary ◽  
Wodzicki Residue ◽  
Hilbert Action

The Kastler–Kalau–Walze theorem, announced by A. Connes, shows that the Wodzicki residue of the inverse square of the Dirac operator is proportional to the Einstein–Hilbert action of general relativity. In this paper, we prove a Kastler–Kalau–Walze type theorem for five-dimensional manifolds with boundary.

scholarly journals The Classical and Quantum Photon Field for Non-compact Manifolds with Boundary and in Possibly Inhomogeneous Media

2021 ◽  
Author(s):  
Alexander Strohmaier
Keyword(s):  
Differential Forms ◽  
Integral Kernel ◽  
Inhomogeneous Media ◽  
Beltrami Operator ◽  
Compact Manifolds ◽  
Energy Tensor ◽  
Manifolds With Boundary ◽  
Important Special Case ◽  
Zero Modes ◽  
Photon Field

AbstractIn this article I give a rigorous construction of the classical and quantum photon field on non-compact manifolds with boundary and in possibly inhomogeneous media. Such a construction is complicated by zero-modes that appear in the presence of non-trivial topology of the manifold or the boundary. An important special case is $${\mathbb {R}}^3$$ R 3 with obstacles. In this case the zero modes have a direct interpretation in terms of the topology of the obstacle. I give a formula for the renormalised stress energy tensor in terms of an integral kernel of an operator defined by spectral calculus of the Laplace Beltrami operator on differential forms with relative boundary conditions.

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