Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Tomita-Takesaki theory in B(H) with physical applications
Dissertation (MSc)--University of Pretoria, 2019.
Saved in:
| Other Authors: | |
|---|---|
| Format: | Thesis |
| Language: | English |
| Published: |
University of Pretoria
2019
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613534376951808 |
|---|---|
| access_status_str | Open Access |
| author2 | Duvenhage, Rocco |
| author_browse | Duvenhage, Rocco |
| author_facet | Duvenhage, Rocco |
| collection | Thesis |
| dc_rights_str_mv | © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc)--University of Pretoria, 2019. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/72688 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:40.523Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2019 |
| publishDateRange | 2019 |
| publishDateSort | 2019 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/72688 Tomita-Takesaki theory in B(H) with physical applications Duvenhage, Rocco u10049526@tuks.co.za Skosana, Samuel UCTD Dissertation (MSc)--University of Pretoria, 2019. The main aim of this project is to develop a simple, yet mathematically rigorous, version of Tomita-Takesaki theory for the von Neumann algebra B(H ) with a faithful normal state. In Chapter 2 we formulate the theory in terms of tensor products. Even in this fairly general setup we can already attach physical interpretation to the modular objects and J. Namely that, the former, the modular operator induces a unique modular automorphism group t which in turn gives the time-evolution (dynamics) of some physical system. Whereas the modular conjugation implements a time-reversal. Chapter 3 presents an alternative formulation of Tomita-Takesaki theory, unitarily equivalent to the first, but with the space of Hilbert-Schmidt operators as our preferred choice of Hilbert space. To gain further insight into the theory, in Chapter 4, a certain simple physical system is explored. In particular, we look at how the system of an electron in a constant orthogonal magnetic field, together with the associated phenomenon of Landau levels, displays a modular structure in the sense of Tomita-Takesaki theory. In such a case, the algebra of observables and its commutant correspond to the two directions of the magnetic field. Physics MSc Unrestricted 2019-12-13T08:07:32Z 2019-12-13T08:07:32Z 2019/09/05 2019 Dissertation Skosana, S 2019, Tomita-Takesaki theory in B(H) with physical applications, MSc Disertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/72688> S2019 http://hdl.handle.net/2263/72688 en © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Tomita-Takesaki theory in B(H) with physical applications |
| title | Tomita-Takesaki theory in B(H) with physical applications |
| title_full | Tomita-Takesaki theory in B(H) with physical applications |
| title_fullStr | Tomita-Takesaki theory in B(H) with physical applications |
| title_full_unstemmed | Tomita-Takesaki theory in B(H) with physical applications |
| title_short | Tomita-Takesaki theory in B(H) with physical applications |
| title_sort | tomita takesaki theory in b h with physical applications |
| topic | UCTD |
| url | http://hdl.handle.net/2263/72688 |