SOME REMARKS ABOUT SEMICLASSICAL TRACE INVARIANTS AND QUANTUM NORMAL FORMS

Victor Guillemin (1) , Thierry Paul (2)

1 MIT - Massachusetts Institute of Technology
2 DMA - Département de Mathématiques et Applications - ENS Paris

In this paper we explore the connection between semi-classical and quantum Birkhoff canonical forms (BCF) for Schrodinger operators. In particular we give a "non-symbolic" operator theoretic derivation of the quantum Birkhoff canonical form and provide an explicit recipe for expressing the quantum BCF in terms of the semi-classical BCF.

Keywords: Mathematical physics; trace formula; normal forms

Domains: Mathematical Physics [math-ph]; Mathematical Physics [math-ph]; Analysis of PDEs [math.AP]

Victor Guillemin, Thierry Paul. SOME REMARKS ABOUT SEMICLASSICAL TRACE INVARIANTS AND QUANTUM NORMAL FORMS. 2008. ⟨hal-00354474⟩