Algebraic approach to Quantum Field Theory

By R. Brunetti, K. Fredenhagen. 2004

414 citations recorded by the source corpus.

We provide a short introduction to the main features of the algebraic approach to quantum field theories.

View Paper: https://www.semanticscholar.org/paper/f3a32dfda37ace4f4386d4c9329f3ff523161c54

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Citations in the corpus

• Geometrization of quantum mechanics (2007, methodology): “Following the algebraic approach advocated by Segal [3] and Haag and Kastler [4], we consider the space of observables as the collection of all the self-adjoint elements of a C-algebra with identity element.”
• Bulk locality from modular flow (2017, background): “By themselves they are not very nice quantum field theories, see for example [27], but they often arise in an approximate manner.”
• Notes on Some Entanglement Properties of Quantum Field Theory (2018, background): “As explained in [75], there is an intuitive reason for this.”
• The Theory of Quantum Information (2018, background): “The description of quantum states as density operators was proposed independently by von Neumann [214] and Landau [141] in 1927, a notion equivalent to that of quantum channels was proposed by Haag and Kastler [86] in 1964, and the definition of measurements that has been adopted in this book was pr”
• Batalin-Vilkovisky Formalism in Perturbative Algebraic Quantum Field Theory (2011, background): “long ago [32,33], and on the basis of causal perturbation theory, as proposed by Stueckelberg [57] and Bogoliubov [13] and rigorously developed by Epstein and Glaser [28], a corresponding disentanglement is possible also for renormalized perturbative quantum field theory [16].”
• The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement (2012, methodology): “The notion of an operation was introduced by Haag and Kastler [70] within the”
• Adiabatic Vacuum States on General Spacetime Manifolds: Definition, Construction, and Physical Properties (2001, background): “Dimock [13] has shown that U 7→ A(U) is a net of local observable algebras in the sense of Haag and Kastler [21], i.”