167 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
The Energy-momentum of a Poisson structure
Consider the quasi-commutative approximation to a noncommutative geometry. It
is shown that there is a natural map from the resulting Poisson structure to
the Riemann curvature of a metric. This map is applied to the study of
high-frequency gravitational radiation. In classical gravity in the WKB
approximation there are two results of interest, a dispersion relation and a
conservation law. Both of these results can be extended to the noncommutative
case, with the difference that they result from a cocycle condition on the
high-frequency contribution to the Poisson structure, not from the field
equations.Comment: 22 page
Lagrangian form of Schr\"odinger equation
Lagrangian formulation of quantum mechanical Schr\"odinger equation is
developed in general and illustrated in the eigenbasis of the Hamiltonian and
in the coordinate representation. The Lagrangian formulation of physically
plausible quantum system results in a well defined second order equation on a
real vector space. The Klein-Gordon equation for a real field is shown to be
the Lagrangian form of the corresponding Schr\"odinger equation.Comment: To appear in Foundation of Physic
Scattering in Noncommutative Quantum Mechanics
We derive the correction due to noncommutativity of space on Born
approximation, then the correction for the case of Yukawa potential is
explicitly calculated. The correction depends on the angle of scattering. Using
partial wave method it is shown that the conservation of the number of
particles in elastic scattering is also valid in noncommutative spaces which
means that the unitarity relation is held in noncommutative spaces. We also
show that the noncommutativity of space has no effect on the optical theorem.
Finally we study Gaussian function potential in noncommutative spaces which
generates delta function potential as .Comment: 7 Pages, no figure, accepted for publication in Modern Physics
Letters
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