Year: 2026
Type: article
Abstract: This article discusses the quantization of linear Hamiltonian systems, a historically rich but under explored line of research. The key idea is that a classical linear Hamiltonian system induces on its phase space a compatible complex structure and scalar product, giving rise to a complex Hilbert space where classical dynamics becomes a one-parameter unitary group. Boson Fock quantization of this group then recovers, up to unitary equivalence, the results of canonical quantization. This expository overview traces the development of this framework from foundational works to modern symplectic perspectives, offering a case study in the dialogue between analysis, geometry, and physics.
Source: Entropy
DOI: 10.3390/e28040384
Authors: Luigi Accardi, Carlo Pandiscia
Institution: University of Rome Tor Vergata
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7147175376
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