Vietnam Journal of Mathematics

, Volume 44, Issue 1, pp 153–180 | Cite as

On the Fixed Point Equation of a Solvable 4D QFT Model

Article

Abstract

The regularisation of the \({\lambda {\upphi }^{4}_{4}}\)-model on noncommutative Moyal space gives rise to a solvable QFT model in which all correlation functions are expressed in terms of the solution of a fixed point problem. We prove that the non-linear operator for the logarithm of the original problem satisfies the assumptions of the Schauder fixed point theorem, thereby completing the solution of the QFT model.

Keywords

Quantum field theory Solvable model Schauder fixed point theorem 

Mathematics Subject Classification (2010)

81T16 81T08 47H10 46B50 

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Fakultät für PhysikUniversität WienWienAustria
  2. 2.Mathematisches Institut der Westfälischen Wilhelms-UniversitätMünsterGermany

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