Positive energy quantization of linear dynamics

Jan Derezinski (1) , Christian Gérard (2)

1 DMP - Department of Mathematical Methods in Physics Varsaw University Poland
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

The abstract mathematical structure behind the positive energy quantization of linear classical systems is described. It is separated into 3 stages: the description of a classical system, the algebraic quantization and the Hilbert space quantization. 4 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 non-interacting quantum fields.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Jan Derezinski, Christian Gérard. Positive energy quantization of linear dynamics. 2009. ⟨hal-00400225⟩