1,719 research outputs found
Modular Theory, Non-Commutative Geometry and Quantum Gravity
This paper contains the first written exposition of some ideas (announced in
a previous survey) on an approach to quantum gravity based on Tomita-Takesaki
modular theory and A. Connes non-commutative geometry aiming at the
reconstruction of spectral geometries from an operational formalism of states
and categories of observables in a covariant theory. Care has been taken to
provide a coverage of the relevant background on modular theory, its
applications in non-commutative geometry and physics and to the detailed
discussion of the main foundational issues raised by the proposal.Comment: Special Issue "Noncommutative Spaces and Fields
A Remark on Gelfand Duality for Spectral Triples
We present a duality between the category of compact Riemannian spin
manifolds (equipped with a given spin bundle and charge conjugation) with
isometries as morphisms and a suitable "metric" category of spectral triples
over commutative pre-C*-algebras. We also construct an embedding of a
"quotient" of the category of spectral triples introduced in
arXiv:math/0502583v1 into the latter metric category. Finally we discuss a
further related duality in the case of orientation and spin-preserving maps
between manifolds of fixed dimension.Comment: 15 pages, AMS-LaTeX2e, results unchanged, several improvements in the
exposition, appendix adde
Enriched Fell Bundles and Spaceoids
We propose a definition of involutive categorical bundle (Fell bundle)
enriched in an involutive monoidal category and we argue that such a structure
is a possible suitable environment for the formalization of different
equivalent versions of spectral data for commutative C*-categories.Comment: 12 pages, AMS-LaTeX2e, to be published in "Proceedings of 2010 RIMS
Thematic Year on Perspectives in Deformation Quantization and Noncommutative
Geometry
A Category of Spectral Triples and Discrete Groups with Length Function
In the context of A. Connes' spectral triples, a suitable notion of morphism
is introduced. Discrete groups with length function provide a natural example
for our definitions. A. Connes' construction of spectral triples for group
algebras is a covariant functor from the category of discrete groups with
length functions to that of spectral triples. Several interesting lines for
future study of the categorical properties of spectral triples and their
variants are suggested.Comment: 23 pages, AMS-LaTeX2
Covariant Sectors with Infinite Dimension and Positivity of the Energy
We consider a Moebius covariant sector, possibly with infinite dimension, of
a local conformal net of von Neumann algebras on the circle. If the sector has
finite index, it has automatically positive energy. In the infinite index case,
we show the spectrum of the energy always to contain the positive real line,
but, as seen by an example, it may contain negative values. We then consider
nets with Haag duality on the real line, or equivalently sectors with
non-solitonic extension to the dual net; we give a criterion for irreducible
sectors to have positive energy, namely this is the case iff there exists an
unbounded Moebius covariant left inverse. As a consequence the class of sectors
with positive energy is stable under composition, conjugation and direct
integral decomposition.Comment: 25 pages, Latex2
an analytical method to simulate the dynamic performances of truncated cone helix ground heat exchangers
Abstract This paper proposes a dynamic analytical method to simulate the thermal performances of truncated cone helix ground heat exchangers (i.e., the so-called "energy baskets"). These ground-coupled devices are attractive solutions to reduce the initial cost of ground-coupled heat pump systems, as they require lower cost to be drilled and installed with respect to traditional boreholes. However, both design methodologies and performance assessment models are still not well developed, producing substantial uncertainties on final operative performances. This work presents a plain evaluation method based on the heat exchangers theory and the analytical solution of the truncated cone helix heat source in a semi-infinite medium. It can be advantageously used to simulate the thermal performance of truncated cone helix ground heat exchangers as a function of helix geometries and operative conditions evolution (e.g., inlet temperature, fluid flow rate, ground temperature…). Specifically, in this paper, we perform a sensitivity analysis of the thermal performances of a case study by varying the main geometrical parameters. Besides, we compare the heat transfer of the reference configuration with an equivalent cylindrical arrangment. The truncated coil configuration is more effective than cylindrical one as the cone aperture reduces the short-circuits between helix pitch and the equivalent thermal resistance with the ground surface. However, obtained results are notably affected by the assumption of an isothermal surface temperature, which leads to a shallow/plain helix/spiral as the best configuration: different conclusions are expected when a time dependent or adiabatic boundary condition will be accounted in the model
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