×

Infinitesimal symmetries in covariant quantum mechanics. (English) Zbl 1406.81047

Dobrev, Vladimir (ed.), Quantum theory and symmetries with Lie theory and its applications in physics. Volume 2. QTS-X/LT-XII, Varna, Bulgaria, June 19–25, 2017. Singapore: Springer (ISBN 978-981-13-2178-8/hbk; 978-981-13-2179-5/ebook). Springer Proceedings in Mathematics & Statistics 255, 319-336 (2018).
Summary: We discuss the Lie algebras of infinitesimal symmetries of the main covariant geometric objects of covariant quantum mechanics: the time form, the hermitian metric, the upper quantum connection, the quantum lagrangian. Indeed, these infinitesimal symmetries are generated, in a covariant way, by the Lie algebra of time preserving conserved special phase functions. Actually, this Lie algebra of special phase functions generates also the Lie algebra of infinitesimal symmetries of the main classical objects: the time form and the cosymplectic 2-form. A natural output of the classification of the quantum symmetries is a covariant approach to quantum operators and to quantum currents associated with special phase functions.
For the entire collection see [Zbl 1403.81002].

MSC:

81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
17B81 Applications of Lie (super)algebras to physics, etc.
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
58A20 Jets in global analysis
PDFBibTeX XMLCite
Full Text: DOI