Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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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