Quantum Mechanics on the Torus, Klein Bottle and Projective Sphere

Christoph Schulte ()
Additional contact information
Christoph Schulte: TU Clausthal, Institut für Theoretische Physik A

A chapter in Symmetries in Science IX, 1997, pp 313-323 from Springer

Abstract: Abstract The Borel quantization shows that there is a topological dependence of the “free” dynamics on the configuration space M,on which a quantum mechanical system is localized. Unitarily inequivalent quantization mappings are classified by elements (α, D) in π l* (M) × R. In the frame work of Borel quantization the quantization parameter D gives rise to a non-linear Schrödinger equation [1, 2], which reduces to a linear one for D = 0. Our procedure is motivated by the isomorphism of elements in π 1*(M) in the set of equivalence classes of complex line bundles with flat connection [3]. Using these flat connections we will construct a Laplacian on the complex line bundle.

Keywords: Line Bundle; Configuration Space; Quantization Parameter; Parallel Section; Klein Bottle (search for similar items in EconPapers)
Date: 1997
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-5921-4_23

Ordering information: This item can be ordered from
http://www.springer.com/9781461559214

DOI: 10.1007/978-1-4615-5921-4_23

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().