An excellent introduction to the mathematics of QFT which is truly a textbook (which can for instance serve as support material in a 1st or 2nd year graduate course in mathematics) is "Quantum Mechanics and Quantum Field Theory, A Mathematical Primer" by … The theory of distributions was used to provide a mathematical framework for quantum field theory (Wightman 1964). The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. The rigged Hilbert space was used to do so for quantum mechanics (Böhm 1966) and then for quantum field theory (Bogoluliubov et al. Its aim is to introduce mathematicians (and, in particular, graduate students) to the mathematical methods of theoretical and experimental quantum eld theory, with an emphasis on coordinate free presentations Ordinary quantum mechanics is based upon real-valued observables which are We will see that the proper mathematical understanding of Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as “What is a QFT?” did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory. This book is an applied pure mathematics textbook on quantum eld theory. From the mathematical point of view, quantum field theory involves several revolutions in structure just as, if not more, severe as the rev- olutionary change involved in the move from classical to quantum ñechanics. 1975). CLASSICAL FIELD THEORY 2.5 Electromagnetic eld The electromagnetic eld tensor, F @ A @ A (2.20)