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Differential forms and the Wodzicki residue for manifolds with boundary
"... Abstract In [3], Connes found a conformal invariant using Wodzicki’s 1density and computed it in the case of 4dimensional manifold without boundary. In [14], Ugalde generalized the Connes ’ result to ndimensional manifold without boundary. In this paper, we generalize the results of [3] and [14] ..."
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Abstract In [3], Connes found a conformal invariant using Wodzicki’s 1density and computed it in the case of 4dimensional manifold without boundary. In [14], Ugalde generalized the Connes ’ result to ndimensional manifold without boundary. In this paper, we generalize the results of [3] and [14] to the case of manifolds with boundary. Subj. Class.: Noncommutative global analysis; Noncommutative differential geometry.
Differential forms and the noncommutative residue for manifolds with boundary in the nonproduct
, 2006
"... Abstract In this paper, for an even dimensional compact manifold with boundary which has the nonproduct metric near the boundary, we use the noncommutative residue to define a conformal invariant pair. For a 4dimensional manifold, we compute this conformal invariant pair under some conditions and ..."
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Abstract In this paper, for an even dimensional compact manifold with boundary which has the nonproduct metric near the boundary, we use the noncommutative residue to define a conformal invariant pair. For a 4dimensional manifold, we compute this conformal invariant pair under some conditions and point out the way of computations in the general.
INDEX AND HOMOLOGY OF PSEUDODIFFERENTIAL OPERATORS ON MANIFOLDS WITH BOUNDARY
"... Abstract. We prove a local index formula for cusppseudodifferential operators on a manifold with boundary. This is known to be equivalent to an index formula for manifolds with cylindrical ends, and hence we obtain a new proof of the classical AtiyahPatodiSinger index theorem for Dirac operators ..."
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Abstract. We prove a local index formula for cusppseudodifferential operators on a manifold with boundary. This is known to be equivalent to an index formula for manifolds with cylindrical ends, and hence we obtain a new proof of the classical AtiyahPatodiSinger index theorem for Dirac operators on manifolds with boundary, as well as an extension of Melrose’s bindex theorem. Our approach is based on an unpublished paper by Melrose and Nistor “Homology of pseudodifferential operators I. Manifolds with boundary ” [39]. We therefore take the opportunity to review some of the results from that paper from the perspective of subsequent research on the Hochschild and cyclic homologies of algebras of pseudodifferential operators and of their applications to index theory.
RENORMALIZATION OF MASSLESS FEYNMAN AMPLITUDES IN CONFIGURATION SPACE
"... A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration space. For a massless quantum field theory (QFT) we use the technique of extending associate homogeneous distributions to complete the renormalization recursion. A ho ..."
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A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration space. For a massless quantum field theory (QFT) we use the technique of extending associate homogeneous distributions to complete the renormalization recursion. A homogeneous (Poincare ́ covariant) amplitude is said to be convergent if it admits a (unique covariant) extension as a homogeneous distribution. For any amplitude without subdivergences – i.e. for a Feynman distribution that is homogeneous off the full (small) diagonal – we define a renormalization invariant residue. Its vanishing is a necessary and sufficient condition for the convergence of such an amplitude. It extends to arbitrary not necessarily primitively divergent Feynman amplitudes. This notion of convergence is finer than the usual power counting criterion and includes cancellation of divergences.
Some Conformal Invariants from the Noncommutative Residue for Manifolds with Boundary ⋆
"... Abstract. We review previous work of Alain Connes, and its extension by the author, on some conformal invariants obtained from the noncommutative residue on even dimensional compact manifolds without boundary. Inspired by recent work of Yong Wang, we also address possible generalizations of these co ..."
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Abstract. We review previous work of Alain Connes, and its extension by the author, on some conformal invariants obtained from the noncommutative residue on even dimensional compact manifolds without boundary. Inspired by recent work of Yong Wang, we also address possible generalizations of these conformal invariants to the setting of compact manifolds with boundary. Key words: manifolds with boundary; noncommutative residue; Fredholm module; conformal invariants 2000 Mathematics Subject Classification: 53A30 1
A KastlerKalauWalze Type Theorem and the Spectral Action for Perturbations of Dirac Operators on Manifolds with Boundary
"... We prove a KastlerKalauWalze type theorem for perturbations of Dirac operators on compact manifolds with or without boundary. As a corollary, we give two kinds of operatortheoretic explanations of the gravitational action on boundary. We also compute the spectral action for Dirac operators with ..."
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We prove a KastlerKalauWalze type theorem for perturbations of Dirac operators on compact manifolds with or without boundary. As a corollary, we give two kinds of operatortheoretic explanations of the gravitational action on boundary. We also compute the spectral action for Dirac operators with twoform perturbations on 4dimensional compact manifolds.