Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion

Details Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion

2000-01-20

arxiv.org/abs/hep-th/0001129v1

Commun.Math.Phys. 219 (2001) 5-30

Physics

High Energy Physics

High Energy Physics - Theory

29 pages

Scientific paper

10.1007/PL00005563

The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system ${\cal A}^{(n)}$ of observables ``up to $n$ loops'' where ${\cal A}^{(0)}$ is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green's functions.

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