Note on the Intermediate Field Representation of \(\phi ^{2k}\) Theory in Zero Dimension

  • Luca Lionni
  • Vincent Rivasseau


This note is a sequel to Rivasseau and Wang (J. Math. Phys. 51, 092304, 2010). We correct the intermediate field representation for the stable \(\phi ^{2k}\) field theory in zero dimension introduced there and extend it to the case of complex conjugate fields. For \(k = 3\) in the complex case we also provide an improved representation which relies on ordinary convergent Gaussian integrals rather than oscillatory integrals.


Constructive field theory Loop vertex expansion Borel summability 

Mathematics Subject Classification (2010)



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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique, CNRS UMR 8627Université Paris XIOrsay CedexFrance

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