Editing Quantum Electrodynamics (Book)
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* Haag-Kastler/C*-algebra based QFTs (continued into Connes' approach) | * Haag-Kastler/C*-algebra based QFTs (continued into Connes' approach) | ||
* Topological QFTs (originating with Atiyah, Witten, and Segal with axiomatic conformal field theory) | * Topological QFTs (originating with Atiyah, Witten, and Segal with axiomatic conformal field theory) | ||
Once some structural understanding of many basic examples of QFTs was achieved, starting with the S-matrix, the "bootstrap" philosophy began where one algebraically specified the relations between observables and their symmetries out of principle. This leads to the perspective of there being a space of QFTs, where CFTs (conformal field theories) are realized as special fixed points of a flow - much like as with phase transitions in statistical mechanics. Alternatively, other physicists try to determine the source of the analytic properties of the S-matrix leading them to vast simplifications in the computations of amplitudes by circumventing their expression as space-integrals. | Once some structural understanding of many basic examples of QFTs was achieved, starting with the S-matrix, the "bootstrap" philosophy began where one algebraically specified the relations between observables and their symmetries out of principle. This leads to the perspective of there being a space of QFTs, where CFTs (conformal field theories) are realized as special fixed points of a flow - much like as with phase transitions in statistical mechanics. Alternatively, other physicists try to determine the source of the analytic properties of the S-matrix leading them to vast simplifications in the computations of amplitudes by circumventing their expression as space-integrals. |