192 research outputs found
Moyal Planes are Spectral Triples
Axioms for nonunital spectral triples, extending those introduced in the
unital case by Connes, are proposed. As a guide, and for the sake of their
importance in noncommutative quantum field theory, the spaces endowed
with Moyal products are intensively investigated. Some physical applications,
such as the construction of noncommutative Wick monomials and the computation
of the Connes--Lott functional action, are given for these noncommutative
hyperplanes.Comment: Latex, 54 pages. Version 3 with Moyal-Wick section update
Induced Gauge Theory on a Noncommutative Space
We consider a scalar theory on canonically deformed Euclidean space
in 4 dimensions with an additional oscillator potential. This model is known to
be renormalisable. An exterior gauge field is coupled in a gauge invariant
manner to the scalar field. We extract the dynamics for the gauge field from
the divergent terms of the 1-loop effective action using a matrix basis and
propose an action for the noncommutative gauge theory, which is a candidate for
a renormalisable model.Comment: Typos corrected, one reference added; eqn. (49) corrected, one
equation number added; 30 page
Heat kernel and number theory on NC-torus
The heat trace asymptotics on the noncommutative torus, where generalized
Laplacians are made out of left and right regular representations, is fully
determined. It turns out that this question is very sensitive to the
number-theoretical aspect of the deformation parameters. The central condition
we use is of a Diophantine type. More generally, the importance of number
theory is made explicit on a few examples. We apply the results to the spectral
action computation and revisit the UV/IR mixing phenomenon for a scalar theory.
Although we find non-local counterterms in the NC theory on \T^4, we
show that this theory can be made renormalizable at least at one loop, and may
be even beyond
Spectral action beyond the weak-field approximation
The spectral action for a non-compact commutative spectral triple is computed
covariantly in a gauge perturbation up to order 2 in full generality. In the
ultraviolet regime, , the action decays as in any even
dimension.Comment: 17 pages Few misprints correcte
The spectral action for Moyal planes
Extending a result of D.V. Vassilevich, we obtain the asymptotic expansion
for the trace of a "spatially" regularized heat operator associated with a
generalized Laplacian defined with integral Moyal products. The Moyal
hyperplanes corresponding to any skewsymmetric matrix being spectral
triples, the spectral action introduced in noncommutative geometry by A.
Chamseddine and A. Connes is computed. This result generalizes the Connes-Lott
action previously computed by Gayral for symplectic .Comment: 20 pages, no figure, few improvment
Coherent coupling dynamics in a quantum dot microdisk laser
Luminescence intensity autocorrelation (LIA) is employed to investigate
coupling dynamics between (In,Ga)As QDs and a high-Q (~7000) resonator with
ultrafast time resolution (150 fs), below and above the lasing threshold at T =
5 K. For QDs resonant and non-resonant with the cavity we observe both a
six-fold enhancement and a 0.77 times reduction of the spontaneous emission
rate, respectively. In addition, LIA spectroscopy reveals the onset of coherent
coupling at the lasing threshold through qualitative changes in the dynamic
behavior and a tripling of the resonant QD emission rate.Comment: Accepted for publication, Phys. Rev. B Rapid Communications, 11
pages, 4 figure
Probing exciton localization in non-polar GaN/AlN Quantum Dots by single dot optical spectroscopy
We present an optical spectroscopy study of non-polar GaN/AlN quantum dots by
time-resolved photoluminescence and by microphotoluminescence. Isolated quantum
dots exhibit sharp emission lines, with linewidths in the 0.5-2 meV range due
to spectral diffusion. Such linewidths are narrow enough to probe the inelastic
coupling of acoustic phonons to confined carriers as a function of temperature.
This study indicates that the carriers are laterally localized on a scale that
is much smaller than the quantum dot size. This conclusion is further confirmed
by the analysis of the decay time of the luminescence
Constraints, gauge symmetries, and noncommutative gravity in two dimensions
After an introduction into the subject we show how one constructs a canonical
formalism in space-time noncommutative theories which allows to define the
notion of first-class constraints and to analyse gauge symmetries. We use this
formalism to perform a noncommutative deformation of two-dimensional string
gravity (also known as Witten black hole).Comment: Based on lectures given at IFSAP-2004 (St.Petersburg), to be
submitted to Theor. Math. Phys., dedicated to Yu.V.Novozhilov on the occasion
of his 80th birthda
Local covariant quantum field theory over spectral geometries
A framework which combines ideas from Connes' noncommutative geometry, or
spectral geometry, with recent ideas on generally covariant quantum field
theory, is proposed in the present work. A certain type of spectral geometries
modelling (possibly noncommutative) globally hyperbolic spacetimes is
introduced in terms of so-called globally hyperbolic spectral triples. The
concept is further generalized to a category of globally hyperbolic spectral
geometries whose morphisms describe the generalization of isometric embeddings.
Then a local generally covariant quantum field theory is introduced as a
covariant functor between such a category of globally hyperbolic spectral
geometries and the category of involutive algebras (or *-algebras). Thus, a
local covariant quantum field theory over spectral geometries assigns quantum
fields not just to a single noncommutative geometry (or noncommutative
spacetime), but simultaneously to ``all'' spectral geometries, while respecting
the covariance principle demanding that quantum field theories over isomorphic
spectral geometries should also be isomorphic. It is suggested that in a
quantum theory of gravity a particular class of globally hyperbolic spectral
geometries is selected through a dynamical coupling of geometry and matter
compatible with the covariance principle.Comment: 21 pages, 2 figure
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