202 research outputs found
Heat trace for Laplacian type operators with non-scalar symbols
For an elliptic selfadjoint operator acting on a fiber bundle over a
Riemannian manifold, where are -matrices, we develop a
method to compute the heat-trace coefficients which allows to get them by
a pure computational machinery. It is exemplified in dimension 4 by the value
of written both in terms of or diffeomorphic and gauge
invariants. We also answer to the question: when is it possible to get explicit
formulae for ?Comment: 37 pages. v2: misprints corrected, references added, section 5.4
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Crossed product extensions of spectral triples
Given a spectral triple and a -dynamical system where is dense in and is a locally compact
group, we extend the triple to a triplet
on the crossed product which can be promoted to a
modular-type twisted spectral triple within a general procedure exemplified by
two cases: the -algebra of the affine group and the conformal group acting
on a complete Riemannian spin manifold.Comment: Version 3: version to appear in Journal of Noncommutative Geometr
Heat trace and spectral action on the standard Podles sphere
We give a new definition of dimension spectrum for non-regular spectral
triples and compute the exact (i.e. non only the asymptotics) heat-trace of
standard Podles spheres for , study its behavior when
and fully compute its exact spectral action for an explicit class of cut-off
functions.Comment: 44 pages, 1 figur
Fuzzy Mass Relations in the Standard Model
Recently Connes has proposed a new geometric version of the standard model
including a non-commutative charge conjugation. We present a systematic
analysis of the relations among masses and coupling constants in this approach.
In particular, for a given top mass, the Higgs mass is constrained to lie in an
interval. Therefore this constraint is locally stable under renormalization
flow.Comment: 14 pages LaTeX, one figure postscrip
Spectral triples and Toeplitz operators
We give examples of spectral triples, in the sense of A. Connes, constructed
using the algebra of Toeplitz operators on smoothly bounded strictly
pseudoconvex domains in , or the star product for the Berezin-Toeplitz
quantization. Our main tool is the theory of generalized Toeplitz operators on
the boundary of such domains, due to Boutet de Monvel and Guillemin.Comment: 31 page
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