2019/02/26 by Vladimir Georgescu, Georgescu, Vladimir, Andrei Iftimovici +1
Mathematics · #46L60 (Primary) 47A10 #47L90 #81Q10 #81S05 #81S30 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Physics (quant-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1902.10026
openalex publication_date 2019/02/26 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
We show that the C^*-algebra generated by the field operators associated to a symplectic space Ξ is graded by the semilattice of all finite dimensional subspaces of Ξ. If Ξ is finite dimensional we give a simple intrinsic description of the components of the grading, we show that the self-adjoint operators affiliated to the algebra have a many channel structure similar to that of N-body Hamiltonians, in particular their essential spectrum is described by a kind of HVZ theorem, and we point out a large class of operators affiliated to the algebra.