84 research outputs found
Non-Commutative GUTs, Standard Model and C,P,T properties from Seiberg-Witten map
Noncommutative generalizations of Yang-Mills theories using Seiberg-Witten
map are in general not unique. We study these ambiguities and see that SO(10)
GUT, at first order in the noncommutativity parameter \theta, is unique and
therefore is a truly unified theory, while SU(5) is not. We then present the
noncommutative Standard Model compatible with SO(10) GUT. We next study the
reality, hermiticity and C,P,T properties of the Seiberg-Witten map and of
these noncommutative actions at all orders in \theta. This allows to compare
the Standard Model discussed in [5] with the present GUT inspired one.Comment: 9 pages. Presented at the Balkan Workshop 2003, Vrnjacka Banja,
29.8-2.9.2003 and at the 9th Adriatic Meeting, Dubrovnik, 4-14.9.200
Noncommutative Symmetries and Gravity
Spacetime geometry is twisted (deformed) into noncommutative spacetime
geometry, where functions and tensors are now star-multiplied. Consistently,
spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their
deformed Lie algebra structure and that of infinitesimal Poincare'
transformations is defined and explicitly constructed.
This allows to construct a noncommutative theory of gravity.Comment: 26 pages. Lectures given at the workshop `Noncommutative Geometry in
Field and String Theories', Corfu Summer Institute on EPP, September 2005,
Corfu, Greece. Version 2: Marie Curie European Reintegration Grant
MERG-CT-2004-006374 acknowledge
Generalized Extreme Value distribution parameters as dynamical indicators of Stability
We introduce a new dynamical indicator of stability based on the Extreme
Value statistics showing that it provides an insight on the local stability
properties of dynamical systems. The indicator perform faster than other based
on the iteration of the tangent map since it requires only the evolution of the
original systems and, in the chaotic regions, gives further information about
the information dimension of the attractor. A numerical validation of the
method is presented through the analysis of the motions in a Standard map
Gauge theory on kappa-Minkowski revisited: the twist approach
Kappa-Minkowski space-time is an example of noncommutative space-time with
potentially interesting phenomenology. However, the construction of field
theories on this space is plagued with ambiguities. We propose to resolve
certain ambiguities by clarifying the geometrical picture of gauge
transformations on the kappa-Minkowski space-time in the twist approach. We
construct the action for the noncommutative U(1) gauge fields in a geometric
way, as an integral of a maximal form. The effective action with the first
order corrections in the deformation parameter is obtained using the
Seiberg-Witten map to relate noncommutative and commutative degrees of freedom.Comment: Based on talks given at QTS7 (Prague), BW2011 (Donji Milanovac),
Corfu2011, BlagojevicFest (Divcibare
Vacuum polarization in two-dimensional static spacetimes and dimensional reduction
We obtain an analytic approximation for the effective action of a quantum
scalar field in a general static two-dimensional spacetime. We apply this to
the dilaton gravity model resulting from the spherical reduction of a massive,
non-minimally coupled scalar field in the four-dimensional Schwarzschild
geometry. Careful analysis near the event horizon shows the resulting
two-dimensional system to be regular in the Hartle-Hawking state for general
values of the field mass, coupling, and angular momentum, while at spatial
infinity it reduces to a thermal gas at the black-hole temperature.Comment: REVTeX 4, 23 pages. Accepted by PRD. Minor modifications from
original versio
Quantum deformations of Schwarzschild and Schwarzschild-de Sitter spacetimes
A quantum Schwarzschild spacetime and a quantum Schwarzschild-de Sitter
spacetime with cosmological constant are constructed within the
framework of a noncommutative Riemannian geometry developed in an earlier
publication. The metrics and curvatures of the quantum Schwarzschild spacetime
and the quantum Schwarzschild-de Sitter spacetime are computed. It is shown
that up to the second order in the deformation parameter, the quantum
spacetimes are solutions of a noncommutative Einstein equation which is
proposed in this paper.Comment: 14 pages, final version, to appear in Classical and Quantum Gravit
Quantum Corrections to the Thermodynamics of Charged 2-D Black Holes
We consider one-loop quantum corrections to the thermodynamics of a black
hole in generic 2-dimensional dilaton gravity. The classical action is the most
general diffeomorphism invariant action in 1+1 space-time dimensions that
contains a metric, dilaton, and Abelian gauge field, and having at most second
derivatives of the fields. Quantum corrections are introduced by considering
the effect of matter fields conformally coupled to the metric and non-minimally
coupled to the dilaton. Back reaction of the matter fields (via non-vanishing
trace conformal anomaly) leads to quantum corrections to the black hole
geometry. Quantum corrections also lead to modifications in the gravitational
action and hence in expressions for thermodynamic quantities. One-loop
corrections to both geometry and thermodynamics (energy, entropy) are
calculated for the generic dilaton theory. This formalism is applied to a
charged black hole in spherically symmetric gravity and to a rotating BTZ black
hole.Comment: 36 pages, Latex The calculation has been extended to include general
matter-dilaton coupling. Several references have been adde
Symmetry, Gravity and Noncommutativity
We review some aspects of the implementation of spacetime symmetries in
noncommutative field theories, emphasizing their origin in string theory and
how they may be used to construct theories of gravitation. The geometry of
canonical noncommutative gauge transformations is analysed in detail and it is
shown how noncommutative Yang-Mills theory can be related to a gravity theory.
The construction of twisted spacetime symmetries and their role in constructing
a noncommutative extension of general relativity is described. We also analyse
certain generic features of noncommutative gauge theories on D-branes in curved
spaces, treating several explicit examples of superstring backgrounds.Comment: 52 pages; Invited review article to be published in Classical and
Quantum Gravity; v2: references adde
Scaling of the Critical Function for the Standard Map: Some Numerical Results
The behavior of the critical function for the breakdown of the homotopically
non-trivial invariant (KAM) curves for the standard map, as the rotation number
tends to a rational number, is investigated using a version of Greene's residue
criterion. The results are compared to the analogous ones for the radius of
convergence of the Lindstedt series, in which case rigorous theorems have been
proved. The conjectured interpolation of the critical function in terms of the
Bryuno function is discussed.Comment: 26 pages, 3 figures, 13 table
Numerical convergence of the block-maxima approach to the Generalized Extreme Value distribution
In this paper we perform an analytical and numerical study of Extreme Value
distributions in discrete dynamical systems. In this setting, recent works have
shown how to get a statistics of extremes in agreement with the classical
Extreme Value Theory. We pursue these investigations by giving analytical
expressions of Extreme Value distribution parameters for maps that have an
absolutely continuous invariant measure. We compare these analytical results
with numerical experiments in which we study the convergence to limiting
distributions using the so called block-maxima approach, pointing out in which
cases we obtain robust estimation of parameters. In regular maps for which
mixing properties do not hold, we show that the fitting procedure to the
classical Extreme Value Distribution fails, as expected. However, we obtain an
empirical distribution that can be explained starting from a different
observable function for which Nicolis et al. [2006] have found analytical
results.Comment: 34 pages, 7 figures; Journal of Statistical Physics 201
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