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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.
Jan Dereziński, and Christian Gérard. "Positive energy quantization of linear dynamics." Banach Center Publications 89.1 (2010): 75-104. <http://eudml.org/doc/282254>.
@article{JanDereziński2010, abstract = {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.}, author = {Jan Dereziński, Christian Gérard}, journal = {Banach Center Publications}, keywords = {canonical commutation relations; canonical anticommutation relations; Fock spaces; quantum field theory}, language = {eng}, number = {1}, pages = {75-104}, title = {Positive energy quantization of linear dynamics}, url = {http://eudml.org/doc/282254}, volume = {89}, year = {2010}, }
TY - JOUR AU - Jan Dereziński AU - Christian Gérard TI - Positive energy quantization of linear dynamics JO - Banach Center Publications PY - 2010 VL - 89 IS - 1 SP - 75 EP - 104 AB - 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. LA - eng KW - canonical commutation relations; canonical anticommutation relations; Fock spaces; quantum field theory UR - http://eudml.org/doc/282254 ER -