Geodesic
$q$-Deformed Bi-Local Fields II
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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We study a way of $q$-deformation of the bi-local system, the two particle system bounded by a relativistic harmonic oscillator type of potential, from both points of view of mass spectra and the behavior of scattering amplitudes. In our formulation, the deformation is done so that $P^2$, the square of center of mass momentum, enters into the deformation parameters of relative coordinates. As a result, the wave equation of the bi-local system becomes nonlinear with respect to $P^2$; then, the propagator of the bi-local system suffers significant change so as to get a convergent self energy to the second order. The study is also made on the covariant $q$-deformation in four dimensional spacetime.
Keywords: $q$-deformation; bi-local system; harmonic oscillator; nonlinear wave equation. 
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     author = {Haruki Toyoda and Shigefumi Naka},
     title = {$q${-Deformed} {Bi-Local} {Fields~II}},
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     volume = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a30/}
}
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Haruki Toyoda; Shigefumi Naka. $q$-Deformed Bi-Local Fields II. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a30/

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