Communications in Mathematical Physics

, Volume 107, Issue 4, pp 561–575 | Cite as

A conformal holomorphic field theory

  • Anatol Odzijewicz


A formulation of a field theory on the complex Minkowski space in terms of complex differential geometry is proposed. It is also shown that our model of field theory differs from the standard model on the real Minkowski space only in the limit of high energy.


Neural Network Statistical Physic Field Theory Complex System Nonlinear Dynamics 
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  1. 1.
    Abraham, R., Marsden, J.E.: Foundation of mechanics 2nd ed. Reading, MA: Benjamin 1978Google Scholar
  2. 2.
    Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self-duality in four dimensional Riemannian geometry. Proc. R. Soc. Lond. A362, 425–461 (1978)Google Scholar
  3. 3.
    Gawedzki, K.: Fourier-like kernels in geometric quantization. Dissertationes Mathematicae, p. 128 (1976)Google Scholar
  4. 4.
    Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley 1978Google Scholar
  5. 5.
    Guillemin, V., Sternberg, S.: Geometric asymptoties. Providence, RI: Am. Math. Soc. 1977Google Scholar
  6. 6.
    Jacobsen, H.P., Vergne, M.: Wave and Dirac operator, and representations of the conformal group (preprint)Google Scholar
  7. 7.
    Karpio, A., Kryszeń, A., Odzijewicz, A.: Two-twistor conformal hamiltonian spaces. Will appear in Rep. Math. Phys.Google Scholar
  8. 8.
    Manin, Y.I.: Kalibrovochnye pola i holomorfnaja geometria. Sowremiennye problemy matematyki, Vol. 17, pp. 3–55. M.: Viniti 1981Google Scholar
  9. 9.
    Odzijewicz, A.: A holomorphic field theory. Lett. Math. Phys.8, 329–335 (1984)Google Scholar
  10. 10.
    Odzijewicz, A.: Conformal kinematics and twistor flag spaces. Teubner-Texte zur Mathematik34, 47–55 (1981)Google Scholar
  11. 11.
    Penrose, R., MacCallum, M.A.H.: Twistor theory: An approach to the quantisation of fields and space-time. Phys. Rep. C6, 241–316 (1972)Google Scholar
  12. 12.
    Penrose, R.: The twistor programme. Rep. Math. Phys.12, 65–76 (1977)Google Scholar
  13. 13.
    Rühl, W.: On conformal invariance of interacting fields. Commun. Math. Phys.34, 149–166 (1973)Google Scholar
  14. 14.
    Wells, P.O., Jr.: Hyperfunction solutions of the zero-restmass fields equations. Commun. Math. Phys.78, 567–600 (1981)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Anatol Odzijewicz
    • 1
  1. 1.Institute of PhysicsWarsaw University Division in BialystokBialystokPoland

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