algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
In perturbative quantum field theory the algebra of observables of an interacting field theory constructed as a perturbation of the Wick algebra of observables of a free field theory is called, for emphasis, the interacting field algebra of observables, often just “interacting field algebra”, for short.
In terms of causal perturbation theory, the interacting field algebra is obtained from the free field Wick algebra of observables and the perturbative S-matrix by differentiating Bogoliubov's formula, yielding a Møller operator.
More abstractly, the algebra of observables is the formal deformation quantization (specifically Fedosov deformation quantization) of the interacting field theory (Collini 16, Hawkins-Rejzner 16).
$\,$
As the spacetime support varies, the algebras of interacting field quantum observables spanned via the Bogoliubov formula consistitute a causally local net of observables, hence an instance of perturbative AQFT.
(Dütsch-Fredenhagen 00, section 3, following Brunetti-Fredenhagen 99, section 8, Il’in-Slavnov 78)
For proof see this prop. at S-matrix.
The observation that the pertruabtive interacting field quantum observables form a causally local net of quantum observables is due to
then rediscovered in
and made more explicit in
The observation that these algebras are the formal deformation quantization of the interacting field theory is due to
Giovanni Collini, Fedosov Quantization and Perturbative Quantum Field Theory (arXiv:1603.09626)
Eli Hawkins, Kasia Rejzner, The Star Product in Interacting Quantum Field Theory (arXiv:1612.09157)
Last revised on June 10, 2023 at 10:03:56. See the history of this page for a list of all contributions to it.