Quantum Field Theories (QFT) normally concern particle fields which propagate in space-time according to various differential equations (Dirac, Klein-Gordon, etc.) specific to each field type and derived from an action principle applied to a Lagrangian. Have there been any investigations of more general QFT's whose field does not follow any single propagation diff eq. or have a corresponding Lagrangian? Basically something more general than the simple particle <-> field correspondence derived from classical physics. Seems like something that might have been looked at back in the '30s and '40s, or possibly in condensed matter physics, but I've come up empty so far.
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4Something like unparticle physics or little string theories? – Andrew Aug 07 '21 at 01:53
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3Non-particle QFT and non-lagrangian QFT are not synonymous, but both are plentiful. Related to the non-lagrangian theme: Do “typical” QFT's lack a lagrangian description?, and What is the relationship between different types of quantum field theories?, and How general is the Lagrangian quantization approach to field theory?. – Chiral Anomaly Aug 07 '21 at 02:13
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3In the lagrangian (sort of) but non-particle category, an extreme example is Dikjgraaf-Witten theory. I don't know if that degree of generalization is within the scope of the question, but it is within the scope of one of the prominent modern definitions of QFT (I listed some references about that definition in this question). – Chiral Anomaly Aug 07 '21 at 02:17
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Thanks all. It's been a long time since I looked at Georgi's Unparticle Physics, I'll do that again. All the other links were a great help in clarifying the scope of the question, which was meant to be about QFT's being used successfully to calculate experimental results in some area of physics. – Jim Eshelman Aug 08 '21 at 23:58
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Conformal field theories do not have particle interpretations, and are widely used in condensed matter physics. They also play a key role in our understanding of the QFTs we use in particle physics (which are not conformal themselves, but are best understood as marginal deformations of CFTs).
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Thanks. I reviewed Altland and Simmons on Condensed Matter Field Theory before posting the question and came away with a somewhat different impression about Condensed Matter Field Theory vs. the question. I probably need a much deeper dive there. And as I commented above the question really concerns applied QFT's for calculating experimental results rather than abstract, mathematical or axiomatic investigations. – Jim Eshelman Aug 30 '21 at 23:37