On the fixed point equation of a solvable 4D QFT model

Abstract

The regularisation of the $\lambda {\varphi }_4^4$-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.

arXiv comment24 pages, LaTeX (svjour class), 9 figures

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• Non-commutative Renormalization
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Cited by in corpus (2)

• Solvable 4D noncommutative QFT: phase transitions and quest for reflection positivity
• Aspects of perturbative quantum field theory on non-commutative spaces