1,457 research outputs found
Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces
We study sigma-models on noncommutative spaces, notably on noncommutative
tori. We construct instanton solutions carrying a nontrivial topological charge
q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons
is conjectured to consists of an ordinary torus endowed with a complex
structure times a projective space .Comment: Latex, 10 page
Quantum field theory on projective modules
We propose a general formulation of perturbative quantum field theory on
(finitely generated) projective modules over noncommutative algebras. This is
the analogue of scalar field theories with non-trivial topology in the
noncommutative realm. We treat in detail the case of Heisenberg modules over
noncommutative tori and show how these models can be understood as large
rectangular pxq matrix models, in the limit p/q->theta, where theta is a
possibly irrational number. We find out that the modele is highly sensitive to
the number-theoretical aspect of theta and suffers from an UV/IR-mixing. We
give a way to cure the entanglement and prove one-loop renormalizability.Comment: 52 pages, uses feynm
Optimal combining of ground-based sensors for the purpose of validating satellite-based rainfall estimates
Two problems related to radar rainfall estimation are described. The first part is a description of a preliminary data analysis for the purpose of statistical estimation of rainfall from multiple (radar and raingage) sensors. Raingage, radar, and joint radar-raingage estimation is described, and some results are given. Statistical parameters of rainfall spatial dependence are calculated and discussed in the context of optimal estimation. Quality control of radar data is also described. The second part describes radar scattering by ellipsoidal raindrops. An analytical solution is derived for the Rayleigh scattering regime. Single and volume scattering are presented. Comparison calculations with the known results for spheres and oblate spheroids are shown
Renormalization group-like proof of the universality of the Tutte polynomial for matroids
In this paper we give a new proof of the universality of the Tutte polynomial
for matroids. This proof uses appropriate characters of Hopf algebra of
matroids, algebra introduced by Schmitt (1994). We show that these Hopf algebra
characters are solutions of some differential equations which are of the same
type as the differential equations used to describe the renormalization group
flow in quantum field theory. This approach allows us to also prove, in a
different way, a matroid Tutte polynomial convolution formula published by
Kook, Reiner and Stanton (1999). This FPSAC contribution is an extended
abstract.Comment: 12 pages, 3 figures, conference proceedings, 25th International
Conference on Formal Power Series and Algebraic Combinatorics, Paris, France,
June 201
Exact solitons on noncommutative tori
We construct exact solitons on noncommutative tori for the type of actions
arising from open string field theory. Given any projector that describes an
extremum of the tachyon potential, we interpret the remaining gauge degrees of
freedom as a gauge theory on the projective module determined by the tachyon.
Whenever this module admits a constant curvature connection, it solves exactly
the equations of motion of the effective string field theory. We describe in
detail such a construction on the noncommutative tori. Whereas our exact
solution relies on the coupling to a gauge theory, we comment on the
construction of approximate solutions in the absence of gauge fields.Comment: 22 pages, JHEP style, typos corrected and references improve
Quasi-quantum groups from Kalb-Ramond fields and magnetic amplitudes for strings on orbifolds
We present the general form of the operators that lift the group action on the twisted sectors of a bosonic string on an orbifold , in the presence of a Kalb-Ramond field strength . These operators turn out to generate the quasi-quantum group , introduced in the context of orbifold conformal field theory by R. Dijkgraaf, V. Pasquier and P. Roche. The 3-cocycle entering in the definition of is related to by a series of cohomological equations in a tricomplex combining de Rham, Cech and group coboundaries. We construct magnetic amplitudes for the twisted sectors and show that arises as a consistency condition for the orbifold theory. Finally, we recover discrete torsion as an ambiguity in the lift of the group action to twisted sectors, in accordance with previous results presented by E. Sharpe
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