@article{falconi2018dm,
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, \emph{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
finite-dimensional case. We characterize the cylindrical Wigner measures and the \emph{a priori} properties they
inherit from the corresponding quantum states.},
Author = {Marco Falconi},
Journal = {Doc. Math.},
Fjournal = {Documenta Mathematica},
Title = {{Cylindrical Wigner measures}},
doi = {10.25537/dm.2018v23.1677-1756},
Url = {https://ojs.elibm.org/index.php/dm/article/view/374},
Year = {2018},
archivePrefix ={arXiv},
eprint = {1605.04778},
primaryClass = {math.FA},
volume = {23},
pages = {1677-1756},
}