Year: 1998
Type: conference-paper
Abstract: We first review the historical developments, both in physics and in mathematics, that preceded (and in some sense provided the background of) deformation quantization. Then we describe the birth of the latter theory and its evolution in the past twenty years, insisting on the main conceptual developments and keeping here as much as possible on the physical side. For the physical part the accent is put on its relations to, and relevance for, “conventional” physics. For the mathematical part we concentrate on the questions of existence and equivalence, including most recent developments for general Poisson manifolds; we touch also noncommutative geometry and index theorems, and relations with group theory, including quantum groups. An extensive (though very incomplete) bibliography is appended and includes background mathematical literature.
Source: AIP conference proceedings
DOI: 10.1063/1.57093
Author: Daniel Sternheimer
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2109823722