Communications in Mathematical Physics

, Volume 198, Issue 1, pp 111–156 | Cite as

A Non-Gaussian Fixed Point for φ4 in 4−ε Dimensions

  • D. Brydges
  • J. Dimock
  • T. R. Hurd


We consider the φ4 quantum field theory in four dimensions. The Gaussian part of the measure is modified to simulate 4−ε dimensions where ε is small and positive. We give a renormalization group analysis for the infrared behavior of the resulting model. We find that the Gaussian fixed point is unstable but that there is a hyperbolic non-Gaussian fixed point a distance ?(ε) away. In a neighborhood of this fixed point we construct the stable manifold.


Manifold Field Theory Renormalization Group Group Analysis Stable Manifold 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • D. Brydges
    • 1
  • J. Dimock
    • 2
  • T. R. Hurd
    • 3
  1. 1.Dept. of Mathematics, University of Virginia, Charlottesville, VA 22903, USA.¶E-mail: db5d@faraday.clas.virginia.eduUS
  2. 2.Dept. of Mathematics, SUNY at Buffalo, Buffalo, NY 14214, USA.¶E-mail: dimock@ubunix.acsu.buffalo.eduUS
  3. 3.Dept. of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada.¶E-mail: hurdt@mcmail.cis.mcmaster.caCA

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