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


SIGMA 2 (2006), 031, 11 pages      hep-th/0603020      http://dx.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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References

  1. Yukawa H., Quantum theory of non-local fields. Part I. Free fields, Phys. Rev., 1950, V.77, 219-226.
    Katayama Y., Yukawa H., Theory of elementary particles extended in space and time, Progr. Theoret. Phys. Suppl., 1968, N 41, 1-21.
    Naka S., On the study in Japan of theory of elementary particle extended in space-time, in Proceedings of the International Symposium on Extended Objects and Bound Systems: From Relativistic Description to Phenomenological Application (March 19-21, 1992, Karuizawa, Japan), Editors O. Hara, S. Ishida and S. Naka, World Scientific, 1993, 389-426.
  2. Yukawa H., Structure and mass spectrum of elementary particles. I. General considerations, Phys. Rev., 1953, V.91, 415-416.
    Goto T., Naka S., Kamimura K., On the bi-local model and string model. Theory of elementary particles extended in space-time, Progr. Theoret. Phys. Suppl., 1979, N 67, 69-114 (and reference therein).
  3. Barger V.D., Cline D.B., Phenomenological theories of high energy scattering, W.A. Benjamin, Inc., 1969, p. 41.
  4. Van Hove L., Regge pole and single particle exchange mechanisms in high energy collisions, Phys. Lett. B, 1967, V.24, 183-184.
    Bando M., Inoue T., Takada Y., Tanaka S., The Regge pole hypothesis and an extended particle model, Progr. Theoret. Phys., 1967, V.38, 715-732.
    Ishida S., Otokozawa J., Scattering amplitude in the Ur-citon scheme, Progr. Theoret. Phys., 1974, V.47, 2117-2132.
  5. Takabayasi T., Oscillator model for particles underlying unitary symmetry, Nuovo Cimento, 1964, V.33, 668-672.
  6. Macfarlane A.J., On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q, J. Phys. A: Math. Gen., 1989, V.22, 4581-4588.
  7. Fichtmüller M., Lorek A., Wess J., q-deformed phase space and its lattice structure, Z. Phys. C, 1996, V.71, 533-538.
    Cerchiai B.L., Hinterding R., Madore J., Wess J., The geometry of a q-deformed phase space, Eur. Phys. J. C Part. Fields, 1999, V.8, 533-546.
  8. Sogami I.S., Koizumi K., Mir-Kasimov R.M., q-deformed and c-deformed harmonic oscillators, Progr. Theoret. Phys., 2003, V.110, 819-840.
  9. Chaichian M., Demichev A., Introduction to quantum groups, World Scientific, 1996.
  10. Naka S., Toyoda H., 5 dimensional spacetime with q-deformed extra space, Progr. Theoret. Phys., 2003, V.109, 103-114, hep-th/0209199.
  11. Naka S., Toyoda H., Kimishima A., q-deformed bi-local fields, Progr. Theoret. Phys., 2005, V.113, 645-656, hep-th/0412062.
  12. Goto T., On the interaction of extended particles. Formulation of dreaking and connection of strings, Progr. Theoret. Phys., 1972, V.47, 2090-2106.
  13. Goto T., Naka S., On the vertex function in the bi-local field, Progr. Theoret. Phys., 1974, V.51, 299-308.

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