SIGMA 2 (2006), 031, 11 pages      hep-th/0603020      https://doi.org/10.3842/SIGMA.2006.031

q-Deformed Bi-Local Fields II

Haruki Toyoda ^a and Shigefumi Naka ^b
a) Laboratory of Physics, College of Science and Technology Nihon University, 7-24-1 Narashinodai Funabashi-shi Chiba, Japan
^b) Department of Physics, College of Science and Technology Nihon University, 1-8-14 Kanda-Surugadai Chiyoda-ku Tokyo, Japan

Received December 01, 2005, in final form February 22, 2006; Published online March 02, 2006

Abstract
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 P², 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 P²; 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.

Key words: q-deformation; bi-local system; harmonic oscillator; nonlinear wave equation.

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