A C-algebraic Approach to Interacting Quantum Field Theories

A novel C*-algebraic framework is presented for relativistic quantum field theories, fixed by a Lagrangean. It combines the postulates of local quantum physics, encoded in the Haag–Kastler axioms, with insights gained in the perturbative approach to quantum field theory. Key ingredients are an appro...

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Veröffentlicht in:Communications in mathematical physics Jg. 377; H. 2; S. 947 - 969
Hauptverfasser: Buchholz, Detlev, Fredenhagen, Klaus
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2020
Springer Nature B.V
Schlagworte:
Algebra
Axioms
Classical and Quantum Gravitation
Complex Systems
Field theory
Mathematical and Computational Physics
Mathematical Physics
Operators (mathematics)
Physics
Physics and Astronomy
Quantum field theory
Quantum Physics
Quantum theory
Relativistic effects
Relativistic theory
Relativity
Relativity Theory
Scalars
Theoretical
ISSN:0010-3616, 1432-0916
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Zusammenfassung:A novel C*-algebraic framework is presented for relativistic quantum field theories, fixed by a Lagrangean. It combines the postulates of local quantum physics, encoded in the Haag–Kastler axioms, with insights gained in the perturbative approach to quantum field theory. Key ingredients are an appropriate version of Bogolubov’s relative S -operators and a reformulation of the Schwinger–Dyson equations. These are used to define for any classical relativistic Lagrangean of a scalar field a non-trivial local net of C*-algebras, encoding the resulting interactions at the quantum level. The construction works in any number of space-time dimensions. It reduces the longstanding existence problem of interacting quantum field theories in physical spacetime to the question of whether the C*-algebras so constructed admit suitable states, such as stable ground and equilibrium states. The method is illustrated on the example of a non-interacting field and it is shown how to pass from it within the algebra to interacting theories by relying on a rigorous local version of the interaction picture.
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ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-020-03700-9