66 research outputs found
The one-loop renormalization of the gauge sector in the noncommutative standard model
In this paper we construct a version of the standard model gauge sector on
noncommutative space-time which is one-loop renormalizable to first order in
the expansion in the noncommutativity parameter . The one-loop
renormalizability is obtained by the Seiberg-Witten redefinition of the
noncommutative gauge potential for the model containing the usual six
representations of matter fields of the first generation.Comment: 16 pages, 2 figure
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
Emergent Gravity from Noncommutative Spacetime
We showed before that self-dual electromagnetism in noncommutative (NC)
spacetime is equivalent to self-dual Einstein gravity. This result implies a
striking picture about gravity: Gravity can emerge from electromagnetism in NC
spacetime. Gravity is then a collective phenomenon emerging from gauge fields
living in fuzzy spacetime. We elucidate in some detail why electromagnetism in
NC spacetime should be a theory of gravity. In particular, we show that NC
electromagnetism is realized through the Darboux theorem as a diffeomorphism
symmetry G which is spontaneously broken to symplectomorphism H due to a
background symplectic two-form , giving rise to
NC spacetime. This leads to a natural speculation that the emergent gravity
from NC electromagnetism corresponds to a nonlinear realization G/H of the
diffeomorphism group, more generally its NC deformation. We also find some
evidences that the emergent gravity contains the structure of generalized
complex geometry and NC gravity. To illuminate the emergent gravity, we
illustrate how self-dual NC electromagnetism nicely fits with the twistor space
describing curved self-dual spacetime. We also discuss derivative corrections
of Seiberg-Witten map which give rise to higher order gravity.Comment: 50 pages; Cosmetic revision and updated reference
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
Breakdown of Lorentz Invariance for Spin-1/2 Particle Motion in Curved Space-Time with Applications to Muon Decay
This paper explores the properties of the Pauli-Lubanski spin vector for the
general motion of spin-1/2 particles in curved space-time. Building upon
previously determined results in flat space-time, it is shown that the
associated Casimir scalar for spin possesses both gravitational contributions
and frame-dependent contributions due to non-inertial motion, where the latter
represents a possible quantum violation of Lorentz invariance that becomes
significant at the Compton wavelength scale. When applied to muon decay near
the event horizon of a microscopic Kerr black hole, it is shown that its
differential cross section is strongly affected by curvature, with particular
sensitivity to changes in the black hole's spin angular momentum. In the
absence of curvature, the non-inertial contributions to the decay spectrum are
also identified and explored in detail, where its potential for observation is
highest for large electron opening angles. It is further shown how possible
contributions to noncommutative geometry can emerge from within this formalism
at some undetermined length scale. Surprisingly, while the potential exists to
identify noncommutative effects in muon decay, the relevant terms make no
contribution to the decay spectrum, for reasons which remain unknown.Comment: 19 pages, 15 figures; REVTeX file; v5. corrections to references;
Accepted for publication in Phys. Rev.
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
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
O uso de estratégias focadas em resultados para o controle da poluição hídrica no Brasil
Visual Explorations of Dynamics: the Standard Map
The Macintosh application \textit{StdMap} allows easy exploration of many of
the phenomena of area-preserving mappings. This tutorial explains some of these
phenomena and presents a number of simple experiments centered on the use of
this program.Comment: Corrections in a couple of equations, and updated to the latest
version of StdMa
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