scholarly journals Dirac operators with torsion and the noncommutative residue for manifolds with boundary

2014 ◽  
Vol 81 ◽  
pp. 92-111 ◽  
Author(s):  
Jian Wang ◽  
Yong Wang ◽  
ChunLing Yang
Keyword(s):  
Dirac Operators ◽  
Manifolds With Boundary ◽  
Noncommutative Residue

Twisted dirac operators and Kastler-Kalau-Walze theorems for six-dimensional manifolds with boundary

2020 ◽  
Vol 17 (14) ◽  
pp. 2050211
Author(s):  
Sining Wei ◽  
Yong Wang
Keyword(s):  
Vector Bundle ◽  
Dirac Operators ◽  
Manifolds With Boundary ◽  
Unitary Connection ◽  
Twisted Dirac Operators

In this paper, we establish two kinds of Kastler-Kalau-Walze type theorems for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection on six-dimensional manifolds with boundary.

scholarly journals The Noncommutative Residue for Manifolds with Boundary

1996 ◽  
Vol 142 (1) ◽  
pp. 1-31 ◽  
Author(s):  
Boris V. Fedosov ◽  
François Golse ◽  
Eric Leichtnam ◽  
Elmar Schrohe
Keyword(s):  
Manifolds With Boundary ◽  
Noncommutative Residue

scholarly journals A Kastler-Kalau-Walze Type Theorem and the Spectral Action for Perturbations of Dirac Operators on Manifolds with Boundary

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Yong Wang
Keyword(s):  
Type Theorem ◽  
Dirac Operators ◽  
Compact Manifolds ◽  
Manifolds With Boundary ◽  
Spectral Action ◽  
Gravitational Action

We prove a Kastler-Kalau-Walze type theorem for perturbations of Dirac operators on compact manifolds with or without boundary. As a corollary, we give two kinds of operator-theoretic explanations of the gravitational action on boundary. We also compute the spectral action for Dirac operators with two-form perturbations on 4-dimensional compact manifolds.

Determinants, Manifolds with Boundary and Dirac Operators

1998 ◽  
pp. 423-432
Author(s):  
K. P. Wojciechowski ◽  
S. G. Scott ◽  
G. Morchio ◽  
B. Booss-Bavnbek
Keyword(s):  
Dirac Operators ◽  
Manifolds With Boundary

scholarly journals SPECTRAL ASYMMETRY, ZETA FUNCTIONS, AND THE NONCOMMUTATIVE RESIDUE

2006 ◽  
Vol 17 (09) ◽  
pp. 1065-1090 ◽  
Author(s):  
RAPHAËL PONGE
Keyword(s):  
Zeta Functions ◽  
Dirac Operators ◽  
Local Independence ◽  
Integer Points ◽  
Noncommutative Residue ◽  
Spectral Interpretation ◽  
Spectral Asymmetry ◽  
The Difference ◽  
Hilbert Action

In this paper we study the spectral asymmetry of (possibly nonselfadjoint) elliptic ΨDO's in terms of the difference of zeta functions coming from different cuttings. Refining previous formulas of Wodzicki in the case of odd class elliptic ΨDO's, our main results have several consequence concerning the local independence with respect to the cutting, the regularity at integer points of eta functions and a geometric expression for the spectral asymmetry of Dirac operators which, in particular, yields a new spectral interpretation of the Einstein–Hilbert action in gravity.

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