The resolvent algebra of non-relativistic Bose fields: sectors, morphisms, fields and their dynamics

Detlev Buchholz
July 20, 2018
In a previous article it was shown that non-relativistic Hamiltonians, including largely arbitrary pair potentials, induce an automorphic action of time translations on the C*-algebra generated by the gauge invariant (particle number preserving) observables in the resolvent algebra of a non-relativistic Bose field. In this note these results are extended to the corresponding field algebra, i.e. the C*-algebra generated by the observables and a pair of particle number changing isometries. The underlying strategy of proof relies on ideas developed by Doplicher, Haag and Roberts in the sector analysis of relativistic quantum field theories. A more detailed exposition of these results is in preparation.