Polytopes in all dimensional loop quantum gravity
Abstract The Lasserre’s reconstruction algorithm is extended to the D-polytopes with the construction of their shape space. Thus, the areas of d-skeletons $$(1\le d\le D)$$ ( 1 ≤ d ≤ D ) can be expressed as functions of the areas and normal bi-vectors of the (D-1)-faces of D-polytopes. As weak solut...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-01-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-022-09988-2 |
| _version_ | 1818753778373885952 |
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| author | Gaoping Long Yongge Ma |
| author_facet | Gaoping Long Yongge Ma |
| author_sort | Gaoping Long |
| collection | DOAJ |
| description | Abstract The Lasserre’s reconstruction algorithm is extended to the D-polytopes with the construction of their shape space. Thus, the areas of d-skeletons $$(1\le d\le D)$$ ( 1 ≤ d ≤ D ) can be expressed as functions of the areas and normal bi-vectors of the (D-1)-faces of D-polytopes. As weak solutions of the simplicity constraints in all dimensional loop quantum gravity, the simple coherent intertwiners are employed to describe semiclassical D-polytopes. New general geometric operators based on D-polytopes are proposed by using the Lasserre’s reconstruction algorithm and the coherent intertwiners. Such kind of geometric operators have expected semiclassical property by the definition. The consistent semiclassical limit with respect to the semiclassical D-polytopes can be obtained for the usual D-volume operator in all dimensional loop quantum gravity by fixing its undetermined regularization factor case by case. |
| first_indexed | 2024-12-18T05:12:46Z |
| format | Article |
| id | doaj.art-64ff785dc8fc47cd9a5bd7b91a874233 |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-18T05:12:46Z |
| publishDate | 2022-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-64ff785dc8fc47cd9a5bd7b91a8742332022-12-21T21:19:50ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522022-01-0182111710.1140/epjc/s10052-022-09988-2Polytopes in all dimensional loop quantum gravityGaoping Long0Yongge Ma1School of Physics and Technology, Xinjiang UniversitySchool of Physics and Technology, Xinjiang UniversityAbstract The Lasserre’s reconstruction algorithm is extended to the D-polytopes with the construction of their shape space. Thus, the areas of d-skeletons $$(1\le d\le D)$$ ( 1 ≤ d ≤ D ) can be expressed as functions of the areas and normal bi-vectors of the (D-1)-faces of D-polytopes. As weak solutions of the simplicity constraints in all dimensional loop quantum gravity, the simple coherent intertwiners are employed to describe semiclassical D-polytopes. New general geometric operators based on D-polytopes are proposed by using the Lasserre’s reconstruction algorithm and the coherent intertwiners. Such kind of geometric operators have expected semiclassical property by the definition. The consistent semiclassical limit with respect to the semiclassical D-polytopes can be obtained for the usual D-volume operator in all dimensional loop quantum gravity by fixing its undetermined regularization factor case by case.https://doi.org/10.1140/epjc/s10052-022-09988-2 |
| spellingShingle | Gaoping Long Yongge Ma Polytopes in all dimensional loop quantum gravity European Physical Journal C: Particles and Fields |
| title | Polytopes in all dimensional loop quantum gravity |
| title_full | Polytopes in all dimensional loop quantum gravity |
| title_fullStr | Polytopes in all dimensional loop quantum gravity |
| title_full_unstemmed | Polytopes in all dimensional loop quantum gravity |
| title_short | Polytopes in all dimensional loop quantum gravity |
| title_sort | polytopes in all dimensional loop quantum gravity |
| url | https://doi.org/10.1140/epjc/s10052-022-09988-2 |
| work_keys_str_mv | AT gaopinglong polytopesinalldimensionalloopquantumgravity AT yonggema polytopesinalldimensionalloopquantumgravity |