Book Review: Introduction to axiomatic quantum field theory

Axiomatic Topological Quantum Field Theory

This dissertation provides an introduction to the ideas employed in topological quantum field theory. We illustrate how the field began by considering knot invariants of three-manifolds and demonstrating the consequences of defining such a theory axiomatically. The ideas of category theory are introduced and we show that what we are actually concerned with are symmetric monoidal functors from t...

Introduction to Quantum Field Theory

Introduction to Quantum Field Theory

These notes are intended to supplement the lecture course ‘Field Theory in Condensed Matter’ and are not intended for wider distribution. Any errors or obvious omissions should be communicated to me at [email protected].

Current Trends in Axiomatic Quantum Field Theory

In this article a non–technical survey is given of the present status of Axiomatic Quantum Field Theory and interesting future directions of this approach are outlined. The topics covered are the universal structure of the local algebras of observables, their relation to the underlying fields and the significance of their relative positions. Moreover, the physical interpretation of the theory i...

Axiomatic, Parameterized, Off-Shell Quantum Field Theory

Axiomatic QFT attempts to provide a rigorous mathematical foundation for QFT, and it is the basis for proving some important general results, such as the well-known spin-statistics theorem. Free-field QFT meets the axioms of axiomatic QFT, showing they are consistent. Nevertheless, even after more than 50 years, there is still no known non-trivial theory of quantum fields with interactions in f...