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Quantum Electrodynamics (Book): Difference between revisions
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* 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) | ||
As Costello puts it, QFT based on Lagrangians of fields (and correlator techniques) is the most fundamental. C*-algebra QFT has been used to describe information theoretic aspects of QFT, even near black holes, but yields few concrete techniques in the way of relevant QFT. TQFTs skirt formulating the analytic content of what a QFT is, focusing instead on their emergent topological properties, but goes even further from real physics. They are however a novel topological invariant, so more resources on TQFT will appear here under further algebraic topology. | As Costello puts it, QFT based on Lagrangians of fields (and correlator techniques) is the most fundamental. C*-algebra QFT has been used to describe information theoretic aspects of QFT, even near black holes, but yields few concrete techniques in the way of relevant QFT. TQFTs skirt formulating the analytic content of what a QFT is, focusing instead on their emergent topological properties, but goes even further from real physics. They are however a novel topological invariant, so more resources on TQFT will appear here under further algebraic topology. | ||
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. | |||