1995/08/24 by Mathias Pillin · 13 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Commutative property #Differential (mechanical device) #Differential algebra #Differential calculus #Differential form #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #Quantum #Quantum differential calculus #hep-th #math.QA #q-alg
paper · pdf · doi:10.1007/bf02101181
published in Communications in Mathematical Physics 180(1), 23-38 (Springer Science+Business Media) · 16 pages, latex, no figures
arxiv created 1995/08/24 · openalex publication_date 1996/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Based on the vanishing of the second Hochschild cohomology group of the enveloping algebra of the Heisenberg algebra it is shown that differential algebras coming from quantum groups do not provide a non-trivial deformation of quantum mechanics. For the case of a q-oscillator there exists a deforming map to the classical algebra. It is shown that the differential calculus on quantum planes with involution, i.e. if one works in position-momentum realization, can be mapped on a q-difference calculus on a commutative real space. Although this calculus leads to an interesting discretization it is proved that it can be realized by generators of the undeformed algebra and does not posess a proper group of global transformations.