2001/04/19 by K. Schoenhammer, K. Schönhammer · 7 citations
Mathematics · Physics and Astronomy · #Banach space #Bosonization #Cold Atom Physics and Bose-Einstein Condensates #Commutation #Compact operator #Extension (predicate logic) #Fermion #Field (mathematics) #Finite-rank operator #Ladder operator #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Physics #Position operator #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum mechanics #Quasinormal operator #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.63.245102
published in Physical review. B, Condensed matter 63(24) (American Physical Society) · 9 pages,1 figure
arxiv created 2001/04/19 · openalex publication_date 2001/05/10 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The acceleration theorem for Bloch electrons in a homogenous external field is usually presented using quasiclassical arguments. In quantum-mechanical versions the Heisenberg equations of motion for an operator \stackrel\ensuremath→\mathrmk\ifmmode \else \\fi(t) are presented mostly without properly defining this operator. This leads to the surprising fact that the generally accepted version of the theorem is incorrect for the most natural definition of \stackrel\ensuremath→\mathrmk\ifmmode \else \\fi. This operator is shown not to obey canonical commutation relations with the position operator. A similar result is shown for the phase operators defined via the Klein factors which take care of the change of particle number in the bosonization of the field operator in the description of interacting fermions in one dimension. The phase operators are also shown not to obey canonical commutation relations with the corresponding particle number operators. Implications of this fact are discussed for Tomonaga-Luttinger-type models.