A brief, though complete and self-consistent, introduction to perturbative Algebraic Quantum Field Theory (pAQFT)

Written by one of the leading experts in the field

The reader get all the prerequisites to understand QFT concepts used in cutting edge research in particle physics, cosmology and solid state physics.

A useful reference for mathematicians interested in QFT

Includes supplementary material: [...]

Introduction.- Algebraic approach to quantum theory.- Algebraic quantum mechanics.- Causality.- Haag-Kastler axioms.- pAQFT axioms.- LCQFT.- Kinematical structure.- The space of field configurations.- Functionals on the configuration space.- Fermionic field configurations.- Vector fields.- Functorial interpretation.- Classical theory.- Dynamics.- Natural Lagrangians.- Homological characterization of the solution space.- The net of topological Poisson algabras.- Analogy with classical mechanics.- Deformation quantization.- Star products.- The star product on the space of multivector fields.- Kähler structure.- Interaction.- Outline of the approach.- Scatering matrix and time ordered products.- Renormalization group.- Interacting local nets.- Explicit construction.- Gauge theories.- Classical gauge theory.- Gauge-fixing.- BV formalism.- Effective quantum gravity.- From LCQFT to quantum gravity.- Dynamics and symmetries.- Linearized theory.- Quantization.- Relational observables.- Background independence.