Local atiyah-singer index theorem for families of dirac operators

1989 ◽  
pp. 351-366 ◽  
Author(s):  
Wei-ping Zhang
Keyword(s):  
Dirac Operators ◽  
Index Theorem

scholarly journals An L2-Index Theorem for Dirac Operators on S1×R3

2000 ◽  
Vol 177 (1) ◽  
pp. 203-218 ◽  
Author(s):  
Tom M.W. Nye ◽  
Michael A. Singer
Keyword(s):  
Dirac Operators ◽  
Index Theorem ◽  
L2 Index

scholarly journals GENERALIZED GINSPARG–WILSON ALGEBRA AND INDEX THEOREM ON THE LATTICE

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1931-1941
Author(s):  
KAZUO FUJIKAWA
Keyword(s):  
General Class ◽  
Dirac Operators ◽  
Index Theorem ◽  
Explicit Construction ◽  
Negative Integer ◽  
Chiral Anomaly ◽  
Gauge Fields ◽  
Topological Properties

Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific algebraic realization of the Ginsparg-Wilson relation in the form γ5 (γ5D) + (γ5D)γ5 = 2a2k+1(γ5D)2k+2 where k stands for a non-negative integer. The choice k = 0 corresponds to the commonly discussed Ginsparg-Wilson relation and thus to the overlap operator. It is shown that local chiral anomaly and the instanton-related index of all these operators are identical. The locality of all these Dirac operators for vanishing gauge fields is proved on the basis of explicit construction, but the locality with dynamical gauge fields has not been fully established yet.

scholarly journals A K-theoretic relative index theorem and Callias-type Dirac operators

1995 ◽  
Vol 303 (1) ◽  
pp. 241-279 ◽  
Author(s):  
Ulrich Bunke
Keyword(s):  
Dirac Operators ◽  
Index Theorem ◽  
Relative Index

scholarly journals An index theorem for non-standard Dirac operators

1999 ◽  
Vol 16 (7) ◽  
pp. 2537-2544 ◽  
Author(s):  
Jan-Willem van Holten ◽  
Andrew Waldron ◽  
Kasper Peeters
Keyword(s):  
Dirac Operators ◽  
Index Theorem

scholarly journals An index theorem of Callias type for pseudodifferential operators

2011 ◽  
Vol 8 (3) ◽  
pp. 387-417 ◽  
Author(s):  
Chris Kottke
Keyword(s):  
Pseudodifferential Operators ◽  
Dirac Operators ◽  
Index Theorem ◽  
Symbolic Data ◽  
Manifold With Boundary ◽  
K Theory ◽  
Hermitian Bundle ◽  
Index Formulas

AbstractWe prove an index theorem for families of pseudodifferential operators generalizing those studied by C. Callias, N. Anghel and others. Specifically, we consider operators on a manifold with boundary equipped with an asymptotically conic (scattering) metric, which have the form D + iΦ, where D is elliptic pseudodifferential with Hermitian symbols, and Φ is a Hermitian bundle endomorphism which is invertible at the boundary and commutes with the symbol of D there. The index of such operators is completely determined by the symbolic data over the boundary. We use the scattering calculus of R. Melrose in order to prove our results using methods of topological K-theory, and we devote special attention to the case in which D is a family of Dirac operators, in which case our theorem specializes to give family versions of the previously known index formulas.

scholarly journals Index Theorem for Equivariant Dirac Operators on Noncompact Manifolds

K-Theory ◽  
2002 ◽  
Vol 27 (1) ◽  
pp. 61-101 ◽  
Author(s):  
Maxim Braverman
Keyword(s):  
Dirac Operators ◽  
Index Theorem ◽  
Noncompact Manifolds
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