Limitable Dynamical Groups in Quantum Mechanics. I. General Theory and a Spinless Model

DOI10.1063/1.1664494zbMath0162.58702OpenAlexW1997747291MaRDI QIDQ5546682

O. Melsheimer, H. D. Doebner

Publication date: 1968

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1664494

zbMATH Keywords

irreducible representationsdynamical groupcentral extension of the inhomogeneous Galilei grouplimitable dynamical grouplimitable groupNelson extensionsnoninvariance groupnonrelativistic interacting systemsspectrum-generating algebra

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items

Contractions of low-dimensional Lie algebras, Limitable Dynamical Groups in Quantum Mechanics. II. A Model Including Arbitrary Spin, Remarks on Infinite-Dimensional Representations of the Heisenberg Algebra, Higher symmetry of certain classical quadratic Hamiltonians, Quadratic time dependent Hamiltonians and separation of variables, On dynamical groups: Classification of Lie algebras with Galilei subalgebras, Conjugacy and stability theorems in connection with contraction of Lie algebras, Inönü–Wigner contractions of the real four-dimensional Lie algebras, On the role of semisimple subalgebras in the deformation theory of Lie algebras and their homomorphisms. General theory and applications, A multiplicity theorem for representations of inhomogeneous compact groups, Quantum mechanics in a discrete space-time

Cites Work

• Analytic vectors
• Die Eindeutigkeit der Schrödingerschen Operatoren
• The cohomology structure of an associative ring
• The representations of the oscillator group
• A class of operator algebras which are determined by groups
• On unitary ray representations of continuous groups
• Communication Relations of Quantum Mechanics
• Lie Group of the Strong-Coupling Theory
• On a class of generalized group contractions
• On representations of Lie algebras with unbounded generators
• On the Connection between External and Internal Symmetries of Strongly Interacting Particles
• Deformation and Contraction of Lie Algebras
• Galilei Group and Nonrelativistic Quantum Mechanics
• On Induced Representations of Groups
• On the Contraction of Groups and Their Representations