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Explore a rigorous mathematical analysis of a three-dimensional fermionic field theory model featuring symplectic fermions with fractional kinetic terms in this advanced physics lecture. Delve into the computation of field and density critical exponents while examining the anomalous scaling dimension of the density operator and its analytic properties in relation to the distance parameter ε from the non-interacting Gaussian reference theory. Learn about the construction of scaling operators associated with both field and density components, and discover the proof of scale invariance for their corresponding response functions. Investigate the connections between this fermionic model and conformal field theory (CFT) descriptions, gaining insights into advanced techniques in quantum field theory and statistical mechanics. The presentation draws from collaborative research published in arXiv:2404.14904, offering cutting-edge developments in the mathematical physics of critical phenomena and scaling behavior in three-dimensional fermionic systems.
