|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'503'724
Articles rated: 2609
23 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Group Theoretical Quantization and the Example of a Phase Space S^1 x R^+ | | Martin Bojowald
; Thomas Strobl
; | | Date: |
27 Aug 1999 | | Journal: | J.Math.Phys. 41 (2000) 2537-2567 | | Subject: | quant-ph gr-qc hep-th | | Abstract: | The group theoretical quantization scheme is reconsidered by means of elementary systems. Already the quantization of a particle on a circle shows that the standard procedure has to be supplemented by an additional condition on the admissibility of group actions. A systematic strategy for finding admissible group actions for particular subbundles of cotangent spaces is developed, two-dimensional prototypes of which are T^*R^+ and S^1 x R^+ (interpreted as restrictions of T^*R and T^*S^1 to positive coordinate and momentum, respectively). In this framework (and under an additional, natural condition) an SO_+(1,2)-action on S^1 x R^+ results as the unique admissible group action. For symplectic manifolds which are (specific) parts of phase spaces with known quantum theory a simple projection method of quantization is formulated. For T^*R^+ and S^1 x R^+ equivalent results to those of more established (but more involved) quantization schemes are obtained. The approach may be of interest, e.g., in attempts to quantize gravity theories where demanding nondegenerate metrics of a fixed signature imposes similar constraints. | | Source: | arXiv, quant-ph/9908079 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER