Microcausality in Lorentz-violating states is equivalent to specific analyticity and exponential boundedness of spatial Fourier transforms of commutators, with explicit EFT constraints.
Strocchi, Selected Topics on the General Properties of Quantum Field Theory
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Microcausality without Lorentz invariance
Microcausality in Lorentz-violating states is equivalent to specific analyticity and exponential boundedness of spatial Fourier transforms of commutators, with explicit EFT constraints.