Quantum groups, non-commutative differential geometry and applications

PDF Version Also Available for Download.

Description

The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related sciences. A generalization of unitary time evolution is proposed and studied for a simple 2-level system, leading to non-conservation of microscopic entropy, a phenomenon new to quantum mechanics. A Cartan calculus that combines functions, forms, Lie derivatives and inner derivations along general vector fields into one big algebra is constructed for quantum groups and then extended to quantum planes. The construction of a tangent bundle on a ... continued below

Physical Description

134 p.

Creation Information

Schupp, P. December 9, 1993.

Context

This thesis or dissertation is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this document can be viewed below.

Who

People and organizations associated with either the creation of this thesis or dissertation or its content.

Author

  • Schupp, P. California Univ., Berkeley, CA (United States). Dept. of Physics

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this thesis or dissertation. Follow the links below to find similar items on the Digital Library.

Description

The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related sciences. A generalization of unitary time evolution is proposed and studied for a simple 2-level system, leading to non-conservation of microscopic entropy, a phenomenon new to quantum mechanics. A Cartan calculus that combines functions, forms, Lie derivatives and inner derivations along general vector fields into one big algebra is constructed for quantum groups and then extended to quantum planes. The construction of a tangent bundle on a quantum group manifold and an BRST type approach to quantum group gauge theory are given as further examples of applications. The material is organized in two parts: Part I studies vector fields on quantum groups, emphasizing Hopf algebraic structures, but also introducing a ``quantum geometric`` construction. Using a generalized semi-direct product construction we combine the dual Hopf algebras A of functions and U of left-invariant vector fields into one fully bicovariant algebra of differential operators. The pure braid group is introduced as the commutant of {Delta}(U). It provides invariant maps A {yields} U and thereby bicovariant vector fields, casimirs and metrics. This construction allows the translation of undeformed matrix expressions into their less obvious quantum algebraic counter parts. We study this in detail for quasitriangular Hopf algebras, giving the determinant and orthogonality relation for the ``reflection`` matrix. Part II considers the additional structures of differential forms and finitely generated quantum Lie algebras -- it is devoted to the construction of the Cartan calculus, based on an undeformed Cartan identity.

Physical Description

134 p.

Notes

INIS; OSTI as DE94011358; Paper copy available at OSTI: phone, 865-576-8401, or email, reports@adonis.osti.gov

Source

  • Other Information: TH: Thesis (Ph.D.)

Language

Identifier

Unique identifying numbers for this document in the Digital Library or other systems.

  • Other: DE94011358
  • Report No.: LBL--34942
  • Report No.: UCB-PTH--93/35
  • Grant Number: AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 10148553
  • Archival Resource Key: ark:/67531/metadc1316686

Collections

This document is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

What responsibilities do I have when using this thesis or dissertation?

When

Dates and time periods associated with this thesis or dissertation.

Creation Date

  • December 9, 1993

Added to The UNT Digital Library

  • Nov. 3, 2018, 11:47 a.m.

Usage Statistics

When was this document last used?

Congratulations! It looks like you are the first person to view this item online.

Interact With This Thesis Or Dissertation

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Schupp, P. Quantum groups, non-commutative differential geometry and applications, thesis or dissertation, December 9, 1993; United States. (digital.library.unt.edu/ark:/67531/metadc1316686/: accessed January 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.