Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion
By M. Dütsch, K. Fredenhagen. 2000
148 citations recorded by the source corpus.
Abstract: 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 ?(n) of observables “up to n loops”, where ?(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.
Subfields: Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/db86edd55c28177486742e9ba5b10825233fb0fc
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In Mathematical Physics
In Nuclear and High Energy Physics
Citations in the corpus
- Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime (2001, methodology): “In the case of a scalar field, a construction of these quantities was given recently by Brunetti, Fredenhagen and Köhler [2] and by Brunetti and Fredenhagen [3].”
- Conservation of the Stress Tensor in Perturbative Interacting Quantum Field Theory in Curved Spacetimes (2004, methodology): “Following [2] and [8], we previously explicitly adopted the above viewpoint on Wick polynomials in [15].”
- Local Wick Polynomials and Time Ordered Products¶of Quantum Fields in Curved Spacetime (2001, methodology): “) Our construction of this algebra is essentially a straightforward generalization to curved spacetime (using the methods of [1]) of a construction previously given by [6] in the context of Minkowski space.”
- Renormalized Quantum Yang-Mills Fields in Curved Spacetime (2007, unknown): “The support property follows from the causal factorization property of the time-ordered products A useful combinatorial identity for the retarded produ cts is the Glaser-Lehmann-Zimmermann 7 The fact that, implicit in the notation “ C[[~]]”, the interacting field only contains non-negative powers o ”