Zobrazeno 1 - 10 of 66 pro vyhledávání: '"Bruno Iochum"'
1
Heat coefficient a4 for non minimal Laplace type operators
Autor: Bruno Iochum, Thierry Masson
Publikováno v: Journal of Geometry and Physics. 141:120-146
Given a smooth hermitean vector bundle V of fiber ℂ N over a compact Riemannian manifold and ∇ a covariant derivative on V , let P = − ( | g | − 1 ∕ 2 ∇ μ | g | 1 ∕ 2 g μ ν u ∇ ν + p μ ∇ μ + q ) be a non minimal Laplace type o
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::501d990cdacbbf11aa59e7ef575d3d2a
https://doi.org/10.1016/j.geomphys.2019.03.002
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2
Spectral Action in Noncommutative Geometry
Autor: Michał Eckstein, Bruno Iochum
Publikováno v: Springer, 27, 2018, Springer Briefs in Mathematical Physics, 978-3-319-94787-7. ⟨10.1007/978-3-319-94788-4⟩
Springer International Publishing, 27, 2018, SpringerBriefs in Mathematical Physics, ⟨10.1007/978-3-319-94788-4⟩
SpringerBriefs in Mathematical Physics ISBN: 9783319947877
What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes, deliberately unveiling the answers to these questions. After a brief
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e2d71c4e85956e4bbf0bdf07e74b92d3
https://hal.archives-ouvertes.fr/hal-02005063
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3
Heat asymptotics for nonminimal Laplace type operators and application to noncommutative tori
Autor: Bruno Iochum, Thierry Masson
Publikováno v: Journal of Geometry and Physics
Journal of Geometry and Physics, Elsevier, 2018, 129, pp.1-24. ⟨10.1016/j.geomphys.2018.02.014⟩
Journal of Geometry and Physics, 2018, 129, pp.1-24. ⟨10.1016/j.geomphys.2018.02.014⟩
Let $P$ be a Laplace type operator acting on a smooth hermitean vector bundle $V$ of fiber $\mathbb{C}^N$ over a compact Riemannian manifold given locally by $P= - [g^{\mu\nu} u(x)\partial_\mu\partial_\nu + v^\nu(x)\partial_\nu + w(x)]$ where $u,\,v^
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::67432c858b9143c57aa0b2604639f593
https://hal.archives-ouvertes.fr/hal-01573594/document
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4
The Toolkit for Computations
Autor: Bruno Iochum, Michał Eckstein
Publikováno v: Spectral Action in Noncommutative Geometry ISBN: 9783319947877
In this chapter we introduce a number of mathematical tools, which will prove useful in the spectral action computations. Firstly, we consider the basic properties of some spectral functions via the functional calculus and general Dirichlet series. N
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::5508379d7df1e95b50b4e89ad7dc771e
https://doi.org/10.1007/978-3-319-94788-4_2
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5
Fluctuations of the Spectral Action
Autor: Michał Eckstein, Bruno Iochum
Publikováno v: Spectral Action in Noncommutative Geometry ISBN: 9783319947877
As we have learned in Sect. 1.6 a given spectral triple \((\mathscr {A,H,D})\) ought to be considered as a representative of the entire family of triples \((\mathscr {A},\mathscr {H},\mathscr {D}_{\mathbb {A}})\), which yield equivalent geometries. I
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::8dbac5121cb404214178ed084d514121
https://doi.org/10.1007/978-3-319-94788-4_4
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6
Analytic Properties of Spectral Functions
Autor: Michał Eckstein, Bruno Iochum
Publikováno v: Spectral Action in Noncommutative Geometry ISBN: 9783319947877
In the previous chapter we have witnessed the interplay between the spectral zeta functions and the associated heat traces (cf. Proposition 2.10). We have also learned, in Sect. 2.2.2, how to exploit the Laplace transform to compute the spectral acti
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::6e88313d19cc42254e8c03193e547507
https://doi.org/10.1007/978-3-319-94788-4_3
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8
The Dwelling of the Spectral Action
Autor: Michał Eckstein, Bruno Iochum
Publikováno v: Spectral Action in Noncommutative Geometry ISBN: 9783319947877
The natural habitat of the spectral action is Connes’ noncommutative geometry. Therefore, it is indispensable to lay out its rudiments encoded in the notion of a spectral triple. We will, however, exclusively focus on the aspects of the structure,
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::6dc4ee792ebba5087db100f26e83884b
https://doi.org/10.1007/978-3-319-94788-4_1
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9
Heat trace for Laplace type operators with non-scalar symbols
Autor: Bruno Iochum, Thierry Masson
Publikováno v: Journal of Geometry and Physics
Journal of Geometry and Physics, Elsevier, 2017, 116, pp.90-118. ⟨10.1016/j.geomphys.2017.01.014⟩
Journal of Geometry and Physics, 2017, 116, pp.90-118. ⟨10.1016/j.geomphys.2017.01.014⟩
For an elliptic selfadjoint operator $P =-[u^{\mu\nu}\partial_\mu \partial_\nu +v^\nu \partial_\nu +w]$ acting on a fiber bundle over a Riemannian manifold, where $u,v^\mu,w$ are $N\times N$-matrices, we develop a method to compute the heat-trace coe
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7e2737d49d3a37421767355e563d6b1c
https://hal.archives-ouvertes.fr/hal-01347436/document
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10
Spectral Action on SU q (2)
Autor: Andrzej Sitarz, C. Levy, Bruno Iochum
Publikováno v: Communications in Mathematical Physics. 289:107-155
The spectral action on the equivariant real spectral triple over \A(SU_q(2)) is computed explicitly. Properties of the differential calculus arising from the Dirac operator are studied and the results are compared to the commutative case of the spher
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::95d50ca935a97476414021471eef9154
https://doi.org/10.1007/s00220-009-0810-8
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