Algebraic quantum kinematics: Galilean covariance with positive energy confines unequal-time commutation to null sets
The paper develops an operator-algebraic framework to test whether Galilean kinematics can coexist with certain requirements for local algebras and canonical commutation relations. It concludes that Galilean kinematics are structurally obstructed when combined with positive energy spectra, sharper-than-equal-time microcausality, and a canonical commutator defined by a scale h.