The abstract mathematical structure behind the positive energy quantization of linear classical systems is described. It is separated into three stages: the description of a classical system, the algebraic quantization and the Hilbert space quantization. Four kinds of systems are distinguished: neutral bosonic, neutral bosonic, charged bosonic and charged fermionic. The formalism that is described follows closely the usual constructions employed in quantum physics to introduce noninteracting quantum fields.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-4,
author = {Jan Derezi\'nski and Christian G\'erard},
title = {Positive energy quantization of linear dynamics},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {75-104},
zbl = {1214.81279},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-4}
}
Jan Dereziński; Christian Gérard. Positive energy quantization of linear dynamics. Banach Center Publications, Tome 89 (2010) pp. 75-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-4/