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Communications in Mathematical Physics

, Volume 54, Issue 3, pp 193–218 | Cite as

The Euclidean loop expansion for massive λΦ 4 4 : Through one loop

  • David N. Williams
Article

Abstract

As an application of the theory of solutions of the classical, Euclidean field equation, we prove the existence of solutions to the renormalized functional field equation, for the λΦ4 interaction in four Euclidean space dimensions, with non-negative λ and nonzero mass, through orderℏc. That is, we prove that the functional derivative of the connected generating functional is in the Schwartz space Reℒ(R4), when evaluated at external sources in Reℒ, through orderℏc. We also prove the existence of all functional derivatives of the connected generating functional through the same order. All quantities of interest are analytic in the coupling constant at 0≦λ<∞, and continuous in the external source.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Euclidean Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • David N. Williams
    • 1
  1. 1.Randall Laboratory of PhysicsThe University of MichiganAnn ArborUSA

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