Note about the Loop Vertex Expansion for Phi^2k Theory in Zero Dimension

Luca Lionni, Vincent Rivasseau

Published 2016-01-12Version 1

This note is a sequel to "Loop Vertex Expansion for Phi**2K Theory in Zero Dimension" by V. Rivasseau and Zhituo Wang, Journ. Math.Phys. 51 (2010) 092304 and arXiv:1003.1037. We simplify and make more systematic the loop vertex expansion for the stable Phi^2k field theory in zero dimension and we extend it to the case of complex conjugate fields. We also correct a mistake in section 4 of Journ. Math.Phys. 51 (2010) 092304: for k>3 Lemma 4.1 as stated there is wrong but becomes correct by adding a single last step of intermediate field decomposition.