scholarly journals Cyclic cocycles in the spectral action

2021 ◽  
Author(s):  
Teun D. H. van Nuland ◽  
Walter D. van Suijlekom
Keyword(s):  
Spectral Action

scholarly journals A GRID MODEL FOR SHALLOW WATER WAVES

1986 ◽  
Vol 1 (20) ◽  
pp. 20 ◽  
Author(s):  
Leo H. Holthuijsen ◽  
Nico Booij
Keyword(s):  
Wave Propagation ◽  
Water Waves ◽  
Wave Breaking ◽  
Traditional Approach ◽  
High Wind ◽  
Local Wind ◽  
Shallow Water Waves ◽  
Spectral Action ◽  
Mean Wave Period ◽  
Constant Period

Waves in coastal regions can be affected by the bottom, by currents and by the local wind. The traditional approach in numerical modelling of these waves is to compute the wave propagation with so-called wave rays for mono-chromatic waves (one constant period and one deep water direction) and to supplement this with computations of bottom dissipation. This approach has two important disadvantages. Firstly, spectral computations, e.g. to determine a varying mean wave period or varying shortcrestedness, would be rather inefficient in this approach. Secondly, interpretation of the results of the refraction computations is usually cumbersome because of crossing wave rays. The model presented here has been designed to correct these shortcomings: the computations are carried out efficiently for a large number of wave components and the effects of currents, bottom friction, local wind and wave breaking are added. This requires the exploitation of the concept of the spectral action balance equation and numerical wave propagation on a grid rather than along wave rays. The model has been in operation for problems varying from locally generated waves over tidal flats to swell penetration into Norwegian fjords. A comparison with extensive measurements is described for young swell under high wind penetrating the Rhine estuary.

scholarly journals The Spectral Action and Cosmic Topology

2011 ◽  
Vol 304 (1) ◽  
pp. 125-174 ◽  
Author(s):  
Matilde Marcolli ◽  
Elena Pierpaoli ◽  
Kevin Teh
Keyword(s):  
Spectral Action

scholarly journals Spectral action gravity and cosmological models

2017 ◽  
Vol 18 (3-4) ◽  
pp. 226-234 ◽  
Author(s):  
Matilde Marcolli
Keyword(s):  
Cosmological Models ◽  
Spectral Action

scholarly journals STRINGS, NONCOMMUTATIVE GEOMETRY AND THE SIZE OF THE TARGET SPACE

1999 ◽  
Vol 14 (28) ◽  
pp. 4501-4517 ◽  
Author(s):  
FEDELE LIZZI
Keyword(s):  
String Theory ◽  
Dirac Operator ◽  
Noncommutative Geometry ◽  
Low Energy ◽  
Target Space ◽  
World Sheet ◽  
Crucial Point ◽  
Spectral Action ◽  
Energy Eigenvalues ◽  
The World

We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge noninvariant quantity. This generalizes the R ↔ 1/R symmetry in which momenta and windings are exchanged, to the whole O(d,d,ℤ). The crucial point is that, with a transformation, it is possible always to have all of the lowest eigenvalues of the Hamiltonian to be momentum modes. We interpret this in the framework of noncommutative geometry, in which algebras take the place of point spaces, and of the spectral action principle for which the eigenvalues of the Dirac operator are the fundamental objects, out of which the theory is constructed. A quantum observer, in the presence of many low energy eigenvalues of the Dirac operator (and hence of the Hamiltonian) will always interpreted the target space of the string theory as effectively uncompactified.

ERRATUM: "COMPLEXIFIED FRACTIONAL HEAT KERNEL AND PHYSICS BEYOND THE SPECTRAL TRIPLET ACTION IN NON-COMMUTATIVE GEOMETRY"

2010 ◽  
Vol 07 (05) ◽  
pp. 907-908
Author(s):  
AHMAD RAMI EL-NABULSI
Keyword(s):  
Fractional Integral ◽  
Fractional Integration ◽  
Vital Role ◽  
Cosmological Term ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Fractional Operators ◽  
Spectral Action ◽  
Points Of View

From points of view of physics, fractional operators represent a vital role for describing intermediate processes and critical phenomena in physics. Subsequently, fractional Action-like Variational Approach in the sense of Riemann–Liouville fractional integral has lately gained significance in exploring non-conservative dynamical systems found in classical and quantum field theories. Within the same framework, fractional Dirac operators are introduced and the fractional spectral action principle is constructed and some interesting consequences are discussed. In particular, we show that the fractional spectral triplet action is complexified and the disturbing huge cosmological term may be eliminated. The generalization of the problem in view of the generalized fractional integration operators, namely the Erdelyi–Kober fractional integral, is discussed as well.

scholarly journals HIGGS-DILATON LAGRANGIAN FROM SPECTRAL REGULARIZATION

2012 ◽  
Vol 27 (35) ◽  
pp. 1250203 ◽  
Author(s):  
M. A. KURKOV ◽  
FEDELE LIZZI
Keyword(s):  
Collective Modes ◽  
Spectral Action ◽  
Spectral Regularization

In this paper we calculate the full Higgs-dilaton action describing the Weyl anomaly using the bosonic spectral action. This completes the work we started in our previous paper (JHEP1110, 001 (2011)). We also clarify some issues related to the dilaton and its role as collective modes of fermions under bosonization.

scholarly journals A DARK SECTOR EXTENSION OF THE ALMOST-COMMUTATIVE STANDARD MODEL

2014 ◽  
Vol 29 (01) ◽  
pp. 1450005 ◽  
Author(s):  
CHRISTOPH A. STEPHAN
Keyword(s):  
Scalar Field ◽  
Standard Model ◽  
Present Model ◽  
Higgs Field ◽  
Dark Sector ◽  
Spectral Action ◽  
Scalar Particles ◽  
A Value ◽  
The Standard Model ◽  
Model C

We consider an extension of the Standard Model within the framework of Noncommutative Geometry. The model is based on an older model [C. A. Stephan, Phys. Rev. D79, 065013 (2009)] which extends the Standard Model by new fermions, a new U(1)-gauge group and, crucially, a new scalar field which couples to the Higgs field. This new scalar field allows to lower the mass of the Higgs mass from ~170 GeV, as predicted by the Spectral Action for the Standard Model, to a value of 120–130 GeV. The shortcoming of the previous model lay in its inability to meet all the constraints on the gauge couplings implied by the Spectral Action. These shortcomings are cured in the present model which also features a "dark sector" containing fermions and scalar particles.

Black Hole Entropy from Non-Commutative Geometry and Spontaneous Localisation

2019 ◽  
Author(s):  
Tejinder P. Singh ◽  
Palemkota Maithresh
Keyword(s):  
Black Hole ◽  
Black Hole Entropy ◽  
Entangled State ◽  
Schwarzschild Black Hole ◽  
Spectral Action ◽  
Black Hole Evaporation ◽  
Gravitational Action ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Gravitational Entropy

In our recently proposed theory of quantum gravity, a black hole arises from the spontaneous localisation of an entangled state of a large number of atoms of space-time-matter [STM]. Prior to localisation, the non-commutative curvature of an STM atom is described by the spectral action of non-commutative geometry. By using the techniques of statistical thermodynamics from trace dynamics, we show that the gravitational entropy of a Schwarzschild black hole results from the microstates of the entangled STM atoms and is given (subject to certain assumptions) by the classical Euclidean gravitational action. This action, in turn, equals the Bekenstein-Hawking entropy (Area/$4{L_P}^2$) of the black hole. We argue that spontaneous localisation is related to black-hole evaporation through the fluctuation-dissipation theorem.

scholarly journals The Spectral Action Principle

1997 ◽  
Vol 186 (3) ◽  
pp. 731-750 ◽  
Author(s):  
A. H. Chamseddine ◽  
A. Connes
Keyword(s):  
Action Principle ◽  
Spectral Action
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