129 research outputs found
Connes-Lott model building on the two-sphere
In this work we examine generalized Connes-Lott models on the two-sphere. The
Hilbert space of the continuum spectral triple is taken as the space of
sections of a twisted spinor bundle, allowing for nontrivial topological
structure (magnetic monopoles). The finitely generated projective module over
the full algebra is also taken as topologically non-trivial, which is possible
over . We also construct a real spectral triple enlarging this Hilbert
space to include "particle" and "anti-particle" fields.Comment: 57 pages, LATE
The Connes-Lott program on the sphere
We describe the classical Schwinger model as a study of the projective
modules over the algebra of complex-valued functions on the sphere. On these
modules, classified by , we construct hermitian connections with
values in the universal differential envelope which leads us to the Schwinger
model on the sphere. The Connes-Lott program is then applied using the Hilbert
space of complexified inhomogeneous forms with its Atiyah-Kaehler structure. It
splits in two minimal left ideals of the Clifford algebra preserved by the
Dirac-Kaehler operator D=i(d-delta). The induced representation of the
universal differential envelope, in order to recover its differential
structure, is divided by the unwanted differential ideal and the obtained
quotient is the usual complexified de Rham exterior algebra over the sphere
with Clifford action on the "spinors" of the Hilbert space. The subsequent
steps of the Connes-Lott program allow to define a matter action, and the field
action is obtained using the Dixmier trace which reduces to the integral of the
curvature squared.Comment: 34 pages, Latex, submitted for publicatio
Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry
We generalize the formulation of non-commutative quantum mechanics to three
dimensional non-commutative space. Particular attention is paid to the
identification of the quantum Hilbert space in which the physical states of the
system are to be represented, the construction of the representation of the
rotation group on this space, the deformation of the Leibnitz rule accompanying
this representation and the implied necessity of deforming the co-product to
restore the rotation symmetry automorphism. This also implies the breaking of
rotational invariance on the level of the Schroedinger action and equation as
well as the Hamiltonian, even for rotational invariant potentials. For
rotational invariant potentials the symmetry breaking results purely from the
deformation in the sense that the commutator of the Hamiltonian and angular
momentum is proportional to the deformation.Comment: 21 page
Efficient variational contraction of two dimensional tensor networks with a non trivial unit cell
Tensor network states provide an efficient class of states that faithfully
capture strongly correlated quantum models and systems in classical statistical
mechanics. While tensor networks can now be seen as becoming standard tools in
the description of such complex many-body systems, close to optimal variational
principles based on such states are less obvious to come by. In this work, we
generalize a recently proposed variational uniform matrix product state
algorithm for capturing one-dimensional quantum lattices in the thermodynamic
limit, to the study of regular two-dimensional tensor networks with a
non-trivial unit cell. A key property of the algorithm is a computational
effort that scales linearly rather than exponentially in the size of the unit
cell. We demonstrate the performance of our approach on the computation of the
classical partition functions of the antiferromagnetic Ising model and
interacting dimers on the square lattice, as well as of a quantum doped
resonating valence bond state.Comment: 23 pages, 8 Figure
On Pythagoras' theorem for products of spectral triples
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual
Pythagoras theorem can be formulated in terms of Connes' distance, between pure
states, in the product of commutative spectral triples. We investigate the
generalization to both non pure states and arbitrary spectral triples. We show
that Pythagoras theorem is replaced by some Pythagoras inequalities, that we
prove for the product of arbitrary (i.e. non-necessarily commutative) spectral
triples, assuming only some unitality condition. We show that these
inequalities are optimal, and provide non-unital counter-examples inspired by
K-homology.Comment: Paper slightly shortened to match the published version; Lett. Math.
Phys. 201
A Comparative Study of Different In Vitro Lung Cell Culture Systems to Assess the Most Beneficial Tool for Screening the Potential Adverse Effects of Carbon Nanotubes
To determine the potential inhalatory risk posed by carbon nanotubes (CNTs), a tier-based approach beginning with an in vitro assessment must be adopted. The purpose of this study therefore was to compare 4 commonly used in vitro systems of the human lung (human blood monocyte-derived macrophages [MDM] and monocyte-derived dendritic cells [MDDC], 16HBE14o- epithelial cells, and a sophisticated triple cell co-culture model [TCC-C]) via assessment of the biological impact of different CNTs (single-walled CNTs [SWCNTs] and multiwalled CNTs [MWCNTs]) over 24h. No significant cytotoxicity was observed with any of the cell types tested, although a significant (p < .05), dose-dependent increase in tumor necrosis factor (TNF)-α following SWCNT and MWCNT exposure at concentrations up to 0.02mg/ml to MDM, MDDC, and the TCC-C was found. The concentration of TNF-α released by the MDM and MDDC was significantly higher (p < .05) than the TCC-C. Significant increases (p < .05) in interleukin (IL)-8 were also found for both 16HBE14o- epithelial cells and the TCC-C after SWCNTs and MWCNTs exposure up to 0.02mg/ml. The TCC-C, however, elicited a significantly (p < .05) higher IL-8 release than the epithelial cells. The oxidative potential of both SWCNTs and MWCNTs (0.005-0.02mg/ml) measured by reduced glutathione (GSH) content showed a significant difference (p < .05) between each monoculture and the TCC-C. It was concluded that because only the co-culture system could assess each endpoint adequately, that, in comparison with monoculture systems, multicellular systems that take into consideration important cell type-to-cell type interactions could be used as predictive in vitro screening tools for determining the potential deleterious effects associated with CNT
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