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.
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@article{Buchholz:2018ruh, author = "Buchholz, Detlev", title = "{The Resolvent Algebra of Non-relativistic Bose Fields: Observables, Dynamics and States}", journal = "Commun. Math. Phys.", volume = "362", year = "2018", number = "3", pages = "949-981", doi = "10.1007/s00220-018-3144-6", eprint = "1807.07885", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1807.07885;%%" }