This book is a set of introductory lecture notes on Conformal Field Theory (CFT). Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. The book starts with a non-perturbative formulation of quantum field theory (Wightman axioms) and then, gradually, focuses on the implications of scale and special conformal symmetry, all the way to the modern conformal bootstrap. This approach includes topics such as subtleties of conformal transformations in Minkowski space-time, the construction of Wightman functions and time-ordered correlators both in position- and momentum-space, unitarity bounds derived from the spectral representation, and the appearance of UV and IR divergences. In each chapter, the reader finds useful exercises to master the subject.

This book is meant for graduate students in theoretical physics and for more advanced researchers working in high-energy physics who are not necessarily familiar with the concepts of conformal field theory. Prior knowledge of quantum field theory is needed to master the arguments.

Marc Gilliozis currently a software engineer, working in the IT industry. He got his Ph.D. in the field of particle physics phenomenology from the University of Zurich in 2012 and did a first postdoc experience at the University of Southern Denmark. There, he worked on model building, with a focus on composite Higgs scenarios. After that, he chose a completely different path and started working exclusively on conformal field theory, motivated by the great successes of the conformal bootstrap, obtaining postdoctoral positions at UC Davis, EPFL, and SISSA.  He became specialized in the momentum-space approach to conformal correlation functions.

Introduction.- Classical conformal transformations.- Conformal quantum field theory.- Conformal correlation functions.- State-operator correspondence and OPE.- The conformal bootstrap.- Conclusions.