11,298 research outputs found
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
Two and Three Loops Beta Function of Non Commutative Theory
The simplest non commutative renormalizable field theory, the
model on four dimensional Moyal space with harmonic potential is asymptotically
safe at one loop, as shown by H. Grosse and R. Wulkenhaar. We extend this
result up to three loops. If this remains true at any loop, it should allow a
full non perturbative construction of this model.Comment: 24 pages, 7 figure
Spin dependent fragmentation function at Belle
The measurement of the so far unknown chiral-odd quark transverse spin
distribution in either semi-inclusive DIS (SIDIS) or inclusive measurements in
pp collisions at RHIC has an additional chiral-odd fragmentation function
appearing in the cross section. These chiral-odd fragmentation functions (FF)
can for example be the so-called Collins FF or the Interference FF. HERMES has
given a first hint that these FFs are nonzero, however in order to measure the
transversity one needs these FFs to be precisely known. We have used 29.0
fb of data collected by the Belle experiment at the KEKB
collider to measure azimuthal asymmetries for different charge combinations of
pion pairs and thus access the Collins FF.Comment: Results presented at the DIS 2006 conference in Tsukuba, Japa
Coplanar constant mean curvature surfaces
We consider constant mean curvature surfaces of finite topology, properly
embedded in three-space in the sense of Alexandrov. Such surfaces with three
ends and genus zero were constructed and completely classified by the authors
in arXiv:math.DG/0102183. Here we extend the arguments to the case of an
arbitrary number of ends, under the assumption that the asymptotic axes of the
ends lie in a common plane: we construct and classify the entire family of
these genus-zero coplanar constant mean curvature surfaces.Comment: 35 pages, 10 figures; minor revisions including one new figure; to
appear in Comm. Anal. Geo
Triunduloids: Embedded constant mean curvature surfaces with three ends and genus zero
In 1841, Delaunay constructed the embedded surfaces of revolution with
constant mean curvature (CMC); these unduloids have genus zero and are now
known to be the only embedded CMC surfaces with two ends and finite genus.
Here, we construct the complete family of embedded CMC surfaces with three ends
and genus zero; they are classified using their asymptotic necksizes. We work
in a class slightly more general than embedded surfaces, namely immersed
surfaces which bound an immersed three-manifold, as introduced by Alexandrov.Comment: LaTeX, 22 pages, 2 figures (8 ps files); full version of our
announcement math.DG/9903101; final version (minor revisions) to appear in
Crelle's J. reine angew. Mat
Constant mean curvature surfaces with three ends
We announce the classification of complete, almost embedded surfaces of
constant mean curvature, with three ends and genus zero: they are classified by
triples of points on the sphere whose distances are the asymptotic necksizes of
the three ends.Comment: LaTex, 4 pages, 1 postscript figur
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
Regularization of 2d supersymmetric Yang-Mills theory via non commutative geometry
The non commutative geometry is a possible framework to regularize Quantum
Field Theory in a nonperturbative way. This idea is an extension of the lattice
approximation by non commutativity that allows to preserve symmetries. The
supersymmetric version is also studied and more precisely in the case of the
Schwinger model on supersphere [14]. This paper is a generalization of this
latter work to more general gauge groups
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