10,503 research outputs found
Space-Time from the spectral point of view
We develop the spectral point of view on geometry based on the formalism of
quantum physics. We start from the simple physical question of specifying our
position in space and explain how the spectral geometric point of view provides
a new paradigm to model space-time whose fine structure can be encoded by a
finite geometry. The classification of the irreducible finite geometries of
KO-dimension 6 singles out a ``symplectic--unitary" candidate F, which when
used as the fine texture of space-time delivers from pure gravity on M x F the
Standard Model coupled to gravity and, once extrapolated to unification scale,
gives testable predictions.Comment: 19 pages. To appear in the Proceedings of the 12th Marcel Grossmann
meetin
The Spectral Action Principle
We propose a new action principle to be associated with a noncommutative
space (\Ac ,\Hc ,D). The universal formula for the spectral action is (\psi
,D\psi) + \Trace (\chi (D / \Lb)) where is a spinor on the Hilbert
space, \Lb is a scale and a positive function. When this principle is
applied to the noncommutative space defined by the spectrum of the standard
model one obtains the standard model action coupled to Einstein plus Weyl
gravity. There are relations between the gauge coupling constants identical to
those of as well as the Higgs self-coupling, to be taken at a fixed
high energy scale.Comment: 27 pages, Tex fil
Computational characterization and prediction of metal-organic framework properties
In this introductory review, we give an overview of the computational
chemistry methods commonly used in the field of metal-organic frameworks
(MOFs), to describe or predict the structures themselves and characterize their
various properties, either at the quantum chemical level or through classical
molecular simulation. We discuss the methods for the prediction of crystal
structures, geometrical properties and large-scale screening of hypothetical
MOFs, as well as their thermal and mechanical properties. A separate section
deals with the simulation of adsorption of fluids and fluid mixtures in MOFs
Gravity and the standard model with neutrino mixing
We present an effective unified theory based on noncommutative geometry for
the standard model with neutrino mixing, minimally coupled to gravity. The
unification is based on the symplectic unitary group in Hilbert space and on
the spectral action. It yields all the detailed structure of the standard model
with several predictions at unification scale. Besides the familiar predictions
for the gauge couplings as for GUT theories, it predicts the Higgs scattering
parameter and the sum of the squares of Yukawa couplings. From these relations
one can extract predictions at low energy, giving in particular a Higgs mass
around 170 GeV and a top mass compatible with present experimental value. The
geometric picture that emerges is that space-time is the product of an ordinary
spin manifold (for which the theory would deliver Einstein gravity) by a finite
noncommutative geometry F. The discrete space F is of KO-dimension 6 modulo 8
and of metric dimension 0, and accounts for all the intricacies of the standard
model with its spontaneous symmetry breaking Higgs sector.Comment: 71 pages, 7 figure
Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
The purpose of this letter is to remove the arbitrariness of the ad hoc
choice of the algebra and its representation in the noncommutative approach to
the Standard Model, which was begging for a conceptual explanation. We assume
as before that space-time is the product of a four-dimensional manifold by a
finite noncommmutative space F. The spectral action is the pure gravitational
action for the product space. To remove the above arbitrariness, we classify
the irreducibe geometries F consistent with imposing reality and chiral
conditions on spinors, to avoid the fermion doubling problem, which amounts to
have total dimension 10 (in the K-theoretic sense). It gives, almost uniquely,
the Standard Model with all its details, predicting the number of fermions per
generation to be 16, their representations and the Higgs breaking mechanism,
with very little input. The geometrical model is valid at the unification
scale, and has relations connecting the gauge couplings to each other and to
the Higgs coupling. This gives a prediction of the Higgs mass of around 170 GeV
and a mass relation connecting the sum of the square of the masses of the
fermions to the W mass square, which enables us to predict the top quark mass
compatible with the measured experimental value. We thus manage to have the
advantages of both SO(10) and Kaluza-Klein unification, without paying the
price of plethora of Higgs fields or the infinite tower of states.Comment: Title change only. The title "A Dress for SM the Beggar" was changed
by the Editor of Physical Review Letter
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