11,138 research outputs found
Dirac Operator on the Quantum Sphere
We construct a Dirac operator on the quantum sphere which is
covariant under the action of . It reduces to Watamuras' Dirac
operator on the fuzzy sphere when . We argue that our Dirac operator
may be useful in constructing invariant field theories on
following the Connes-Lott approach to noncommutative geometry.Comment: 13 page
Response of electrostatic probes to ionized gas flows in a shock tube
In his excellent analysis of electrical measurements in shock tube flows, Hollyer(1) has demonstrated certain pitfalls in the application of conventional Langmuir probe techniques to the evaluation of charge densities in the moving stream of hot gas confined within the tube walls. The purpose of this note is to describe somewhat similar experiments which illustrate other eccentricities in probe behavior under these conditions
Functional Renormalization of Noncommutative Scalar Field Theory
In this paper we apply the Functional Renormalization Group Equation (FRGE)
to the non-commutative scalar field theory proposed by Grosse and Wulkenhaar.
We derive the flow equation in the matrix representation and discuss the theory
space for the self-dual model. The features introduced by the external
dimensionful scale provided by the non-commutativity parameter, originally
pointed out in \cite{Gurau:2009ni}, are discussed in the FRGE context. Using a
technical assumption, but without resorting to any truncation, it is then shown
that the theory is asymptotically safe for suitably small values of the
coupling, recovering the result of \cite{disertori:2007}. Finally, we
show how the FRGE can be easily used to compute the one loop beta-functions of
the duality covariant model.Comment: 38 pages, no figures, LaTe
On Finite 4D Quantum Field Theory in Non-Commutative Geometry
The truncated 4-dimensional sphere and the action of the
self-interacting scalar field on it are constructed. The path integral
quantization is performed while simultaneously keeping the SO(5) symmetry and
the finite number of degrees of freedom. The usual field theory UV-divergences
are manifestly absent.Comment: 18 pages, LaTeX, few misprints are corrected; one section is remove
Noncommutative Induced Gauge Theories on Moyal Spaces
Noncommutative field theories on Moyal spaces can be conveniently handled
within a framework of noncommutative geometry. Several renormalisable matter
field theories that are now identified are briefly reviewed. The construction
of renormalisable gauge theories on these noncommutative Moyal spaces, which
remains so far a challenging problem, is then closely examined. The computation
in 4-D of the one-loop effective gauge theory generated from the integration
over a scalar field appearing in a renormalisable theory minimally coupled to
an external gauge potential is presented. The gauge invariant effective action
is found to involve, beyond the expected noncommutative version of the pure
Yang-Mills action, additional terms that may be interpreted as the gauge theory
counterpart of the harmonic term, which for the noncommutative -theory
on Moyal space ensures renormalisability. A class of possible candidates for
renormalisable gauge theory actions defined on Moyal space is presented and
discussed.Comment: 24 pages, 6 figures. Talk given at the "International Conference on
Noncommutative Geometry and Physics", April 2007, Orsay (France). References
updated. To appear in J. Phys. Conf. Se
Noncommutative QFT and Renormalization
Field theories on deformed spaces suffer from the IR/UV mixing and
renormalization is generically spoiled. In work with R. Wulkenhaar, one of us
realized a way to cure this disease by adding one more marginal operator. We
review these ideas, show the application to models and use the heat
kernel expansion methods for a scalar field theory coupled to an external gauge
field on a -deformed space and derive noncommutative gauge field
actions.Comment: To appear in the proceedings of the Workshop "Noncommutative Geometry
in Field and String Theory", Corfu, 2005 (Greece
Beta Power May Mediate the Effect of Gamma-TACS on Motor Performance
Transcranial alternating current stimulation (tACS) is becoming an important
method in the field of motor rehabilitation because of its ability to
non-invasively influence ongoing brain oscillations at arbitrary frequencies.
However, substantial variations in its effect across individuals are reported,
making tACS a currently unreliable treatment tool. One reason for this
variability is the lack of knowledge about the exact way tACS entrains and
interacts with ongoing brain oscillations. The present crossover stimulation
study on 20 healthy subjects contributes to the understanding of
cross-frequency effects of gamma (70 Hz) tACS over the contralateral motor
cortex by providing empirical evidence which is consistent with a role of low-
(12~-20 Hz) and high- (20-~30 Hz) beta power as a mediator of gamma-tACS on
motor performance.Comment: 7 pages, 5 figures, in Proceedings of IEEE Engineering in Medicine
and Biology Conference, July 2019 (IEEE license notice
On the Effective Action of Noncommutative Yang-Mills Theory
We compute here the Yang-Mills effective action on Moyal space by integrating
over the scalar fields in a noncommutative scalar field theory with harmonic
term, minimally coupled to an external gauge potential. We also explain the
special regularisation scheme chosen here and give some links to the Schwinger
parametric representation. Finally, we discuss the results obtained: a
noncommutative possibly renormalisable Yang-Mills theory.Comment: 19 pages, 6 figures. At the occasion of the "International Conference
on Noncommutative Geometry and Physics", April 2007, Orsay (France). To
appear in J. Phys. Conf. Se
Induced Gauge Theory on a Noncommutative Space
We discuss the calculation of the 1-loop effective action on four
dimensional, canonically deformed Euclidean space. The theory under
consideration is a scalar model with an additional oscillator
potential. This model is known to be re normalisable. Furthermore, we couple an
exterior gauge field to the scalar field and extract the dynamics for the gauge
field from the divergent terms of the 1-loop effective action using a matrix
basis. This results in proposing an action for noncommutative gauge theory,
which is a candidate for a renormalisable model.Comment: 8 page
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