Cylindrical Wigner measures
Abstract
In this paper we study the semiclassical behavior of quantum states acting on the C*algebra of canonical commutation relations, from a general perspective. The aim is to provide a unified and flexible approach to the semiclassical analysis of bosonic systems. We also give a detailed overview of possible applications of this approach to mathematical problems of both axiomatic relativistic quantum field theories and nonrelativistic many body systems. If the theory has infinitely many degrees of freedom, the set of Wigner measures, i.e. the classical counterpart of the set of quantum states, coincides with the set of all cylindrical measures acting on the algebraic dual of the space of test functions for the field, and this reveals a very rich semiclassical structure compared to the finitedimensional case. We characterize the cylindrical Wigner measures and the \emph{a priori} properties they inherit from the corresponding quantum states.
 Publication:

arXiv eprints
 Pub Date:
 May 2016
 arXiv:
 arXiv:1605.04778
 Bibcode:
 2016arXiv160504778F
 Keywords:

 Mathematics  Functional Analysis;
 Mathematical Physics;
 Mathematics  Operator Algebras;
 81S05;
 46L99;
 47L90
 EPrint:
 59 pages