arXiv subjects
Publications and source records attributed to K. Podlaski.
A classification of idempotents in Clifford algebras C(p,q) is presented. It is shown that using isomorphisms between Clifford algebras C(p,q) and appropriate matrix rings, it is possible to classify idempotents in any Clifford algebra into continuous families. These families include primitive idempotents used to generate minimal one sided ideals in Clifford algebras. Some low dimensional examples are discussed.
The detailed study of a quantum free particle on a pointed plane is performed. It is shown that there is no problem with a mysterious ``quantum anticentrifugal force" acting on a free particle on a plane discussed in a very recent paper: M. A. Cirone et al, Phys. Rev. A 65, 022101 (2002), but we deal with a purely topological efect related to distinguishing a point on a plane. The new results are introduced concerning self-adjoint extensions of operators describing the free particle on a pointed plane as well as the role played by discrete symmetries in the analysis of such extensions.