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Nonlinear Spinor Theory in Terms of Vacuum Expectation Values

  • H. Mitter
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 3/1966)

Abstract

We shall consider in these lectures the system of equations for the vacuum expectation values of certain products of field operators (the n-point-functions) of a nonlinear, cubic spinor theory with the field equation
$$ % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa % aaleaacqaHXoqycqaHYoGyaeqaaOGaeqiYdK3aaSbaaSqaaiabek7a % IbqabaGccqGHRaWkcaWGwbWaaSbaaSqaaiabeg7aHjabek7aIjaacY % cacqqHspqOcqaH0oazaeqaaOGaeqiYdK3aa0baaSqaaiabfk9aHcqa % aiaacQcaaaGccqaHipqEdaWgaaWcbaGaeuO0dekabeaakiabeI8a5n % aaBaaaleaacqaH0oazaeqaaOGaeyypa0JaaGimaaaa!555C! D_{\alpha \beta } \psi _\beta + V_{\alpha \beta ,\Upsilon \delta } \psi _\Upsilon ^* \psi _\Upsilon \psi _\delta = 0 $$
(1)

Keywords

Field Equation Light Cone Vacuum Expectation Canonical Theory Renormalizable Theory 
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References

  1. 1.
    Functional techniques have been discussed by various authors. For renormalizable theories see e.g. K. Symanzik, Hercegovi lectures 1962, where more literature can be found.Google Scholar
  2. 2.
    The correlation functions n have been used in field theory by W. Zimmermann, Nuovo Cim. 13, 503 (1959).Google Scholar
  3. 3.
    For literature see footnote 10) in the paper by G.Källén, Acta Physica Austriaca, Suppl. II., 1965. The representation was used also by J. Schwinger in a lecture at Harvard University 1954 (The Theory of Coupled Fields, unpublished lecture notes).Google Scholar
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    A. S. Wightman, Phys. Rev. 101, 860 (1956).MathSciNetADSMATHCrossRefGoogle Scholar
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    I. M. Gel’fand, G. E. Schilow, Verallgemeinerte Funktionen I, Berlin 1960.Google Scholar
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    K. Johnson, Nuovo Cim. 20, 773 (1961).CrossRefGoogle Scholar
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    H. Mitter, Nuovo Cim. 38, 1040 (1965).MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Wien 1966

Authors and Affiliations

  • H. Mitter
    • 1
  1. 1.Max-Planck-Institut für Physik und AstrophysikMünchenDeutschland

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