Published August 2005
| Version v1
Journal article
A constructive algorithm for the Cartan decomposition of SU(2N)
- 1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
- 2. Department of Mathematics, Imperial College London, Prince Consort Road, London, SW7 2BW (United Kingdom)
Description
We present an explicit numerical method to obtain the Cartan-Khaneja-Glaser decomposition of a general element G is a member of SU(2N) in terms of its 'Cartan' and 'non-Cartan' components. This effectively factors G in terms of group elements that belong in SU(2n) with n<N, a procedure that can be iterated down to n=2. We show that every step reduces to solving the zeros of a matrix polynomial, obtained by truncation of the Baker-Campbell-Hausdorff formula, numerically. All computational tasks involved are straightforward and the overall truncation errors are well under control
Additional details
Identifiers
- DOI
- 10.1063/1.2008210;
- arXiv
- arXiv:quant-ph/0505128v2;
Publishing Information
- Journal Title
- Journal of Mathematical Physics
- Journal Volume
- 46
- Journal Issue
- 8
- Journal Page Range
- p. 082108-082108.11
- ISSN
- 0022-2488
- CODEN
- JMAPAQ
INIS
- Country of Publication
- United States
- Country of Input or Organization
- International Atomic Energy Agency (IAEA)
- INIS RN
- 37015340
- Subject category
- S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
- Descriptors DEI
- ALGORITHMS; ERRORS; MATRICES; POLYNOMIALS; QUANTUM MECHANICS; SU-2 GROUPS
- Descriptors DEC
- FUNCTIONS; LIE GROUPS; MATHEMATICAL LOGIC; MECHANICS; SU GROUPS; SYMMETRY GROUPS
Optional Information
- Notes
- (c) 2005 American Institute of Physics