2018/04/20 by Viorel Iftimie, Iftimie, Viorel, Radu Purice +3
Mathematics · #47A60 #Advanced Operator Algebra Research #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Primary 35S05 #Secondary 81Q10 #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1804.07636
openalex publication_date 2018/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a series of papers we have argued that the 'basic' physical procedure of minimal coupling giving the quantum description of a Hamiltonian system interacting with a magnetic field, can be given a very satisfactory mathematical formulation as a twisted Weyl quantization \citeMP2. In this paper we shall present a review of some of these results with some modified proofs that allow a special focus on the dependence on the behavior of the magnetic field, having in view possible developments towards problems with unbounded magnetic fields. The main new result is contained in Theorem 2.9 and states that the the symbol of the evolution group of the self-adjoint operator defined by a real elliptic symbol of strictly positive order in a smooth bounded magnetic field is in the associated magnetic Moyal algebra, i.e. leaves invariant the space of Schwartz test functions and its dual