The spacetime approach to quantum field theory. (English) Zbl 0596.58014

Relativité, groupes et topologie II, Les Houches Ec. d’Eté Phys. Théor., Sess. 40, 1983, 381-738 (1984).
[For the entire collection see Zbl 0583.00023.]
This is a lucid course on the covariant perturbative approach for the formal quantization of not only conventional field theories (linear boson and fermion fields) but also of gravity and its supersymmetric extensions with either closed or open super Lie algebras, using essentially the Peierls bracket, this elegant tool for incorporating the canonical algebra into a perturbative covariant structure.
After introducing the prerequisites on superclassical dynamical systems in Part I, the author illustrates the methods in Part II, by considering linear boson and fermion fields in stationary and nonstationary backgrounds. In Part III, non-linear quantized fields are studied at one- loop approximation, in particular Yang-Mills field and gravitational field. Generalized Becchi-Rouet-Stora transformations and effective action are also considered. The difficulties of this approach at higher approximations are however well-known.
The student will find useful the numerous guided exercises at the end of each section and the appendix on supermanifolds.
Reviewer: S.Kichenassamy


58D30 Applications of manifolds of mappings to the sciences
83C45 Quantization of the gravitational field
53C80 Applications of global differential geometry to the sciences


Zbl 0583.00023