Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
The mathematical structure of homogeneous loop quantum cosmology is analyzed, starting with and taking into account the general classification of homogeneous connections not restricted to be Abelian. As a first consequence, it is seen that the usual approach of quantizing Abelian models using spaces...
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| Дата: | 2013 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149374 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1493742019-02-22T01:23:42Z Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models Bojowald, M. The mathematical structure of homogeneous loop quantum cosmology is analyzed, starting with and taking into account the general classification of homogeneous connections not restricted to be Abelian. As a first consequence, it is seen that the usual approach of quantizing Abelian models using spaces of functions on the Bohr compactification of the real line does not capture all properties of homogeneous connections. A new, more general quantization is introduced which applies to non-Abelian models and, in the Abelian case, can be mapped by an isometric, but not unitary, algebra morphism onto common representations making use of the Bohr compactification. Physically, the Bohr compactification of spaces of Abelian connections leads to a degeneracy of edge lengths and representations of holonomies. Lifting this degeneracy, the new quantization gives rise to several dynamical properties, including lattice refinement seen as a direct consequence of state-dependent regularizations of the Hamiltonian constraint of loop quantum gravity. The representation of basic operators - holonomies and fluxes - can be derived from the full theory specialized to lattices. With the new methods of this article, loop quantum cosmology comes closer to the full theory and is in a better position to produce reliable predictions when all quantum effects of the theory are taken into account. 2013 Article Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models / M. Bojowald// Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 101 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R10; 39A14 DOI: http://dx.doi.org/10.3842/SIGMA.2013.082 http://dspace.nbuv.gov.ua/handle/123456789/149374 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The mathematical structure of homogeneous loop quantum cosmology is analyzed, starting with and taking into account the general classification of homogeneous connections not restricted to be Abelian. As a first consequence, it is seen that the usual approach of quantizing Abelian models using spaces of functions on the Bohr compactification of the real line does not capture all properties of homogeneous connections. A new, more general quantization is introduced which applies to non-Abelian models and, in the Abelian case, can be mapped by an isometric, but not unitary, algebra morphism onto common representations making use of the Bohr compactification. Physically, the Bohr compactification of spaces of Abelian connections leads to a degeneracy of edge lengths and representations of holonomies. Lifting this degeneracy, the new quantization gives rise to several dynamical properties, including lattice refinement seen as a direct consequence of state-dependent regularizations of the Hamiltonian constraint of loop quantum gravity. The representation of basic operators - holonomies and fluxes - can be derived from the full theory specialized to lattices. With the new methods of this article, loop quantum cosmology comes closer to the full theory and is in a better position to produce reliable predictions when all quantum effects of the theory are taken into account. |
| format |
Article |
| author |
Bojowald, M. |
| spellingShingle |
Bojowald, M. Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Bojowald, M. |
| author_sort |
Bojowald, M. |
| title |
Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models |
| title_short |
Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models |
| title_full |
Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models |
| title_fullStr |
Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models |
| title_full_unstemmed |
Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models |
| title_sort |
mathematical structure of loop quantum cosmology: homogeneous models |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149374 |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT bojowaldm mathematicalstructureofloopquantumcosmologyhomogeneousmodels |
| first_indexed |
2023-05-20T17:32:51Z |
| last_indexed |
2023-05-20T17:32:51Z |
| _version_ |
1796153542679986176 |