Positive energy quantization of linear dynamics
Jan Derezinski (DMP), Christian G\'erard (LM-Orsay)
TL;DR
This paper details a structured approach to positive energy quantization of linear classical systems, covering classical description, algebraic quantization, and Hilbert space quantization, applicable to various bosonic and fermionic systems.
Contribution
It introduces a comprehensive formalism for positive energy quantization tailored to different types of linear systems, extending standard quantum field constructions.
Findings
Unified framework for quantizing neutral and charged bosonic and fermionic systems
Clarification of the three-stage quantization process for linear systems
Formalism aligns with conventional quantum field theory methods
Abstract
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.
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