## Abstract

Quantum field theory is an important research area in theoretical physics, with a wide range of applications and an impressive agreement with experiment. Despite this success, the mathematical foundations of this theory are still under investigation and many fundamental questions remain open. The rapid development of the field makes it difficult to find textbooks which are up to date with all the recent advances, especially if one looks for a mathematically rigorous approach. It is a common misconception that working with QFT necessarily implies doing something “not-well defined”, while in fact most of the formal manipulations presented in the physics literature can be made completely rigorous.

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