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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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).

  • $\begingroup$ 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. $\endgroup$ Commented Aug 30, 2021 at 23:37

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