Axiomatic foundations of Galilean quantum field theories (Q1768319)

A `realistic' axiomatisation of Galilean Quantum Field Theory (GQFT) is presented which treats fields as real objects with certain properties regarding transformations and inter-relations. The presentation is fully formalised and the axioms rest mainly on (Galilei-) group theory, distributions, and rigged Hilbert space. Main (well known) results derived are the Bargmann mass superselection rule and related constructive constraints on possible GQFTs. It is shown that GQFT in general does not contain spin-statistics relations. Related work of the authors regards axiomatisation of relativistic QFT by \textit{G. Puccini} and \textit{H. Vucetich} [Found. Phys. 34, No. 4, 643--667 (2004; Zbl 1072.81044)].