Intersecting Quantum Gravity with Noncommutative Geometry - a Review
We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holo...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
National Academy of Science of Ukraine
2012-03-01
|
| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2012.018 |
| _version_ | 1819208097365753856 |
|---|---|
| author | Johannes Aastrup Jesper Møller Grimstrup |
| author_facet | Johannes Aastrup Jesper Møller Grimstrup |
| author_sort | Johannes Aastrup |
| collection | DOAJ |
| description | We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holonomy loops. The spectral triple, which encodes the kinematics of quantum gravity, gives rise to a natural class of semiclassical states which entail emerging fermionic degrees of freedom. In the particular semiclassical approximation where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. We end the paper with an extended outlook section. |
| first_indexed | 2024-12-23T05:33:58Z |
| format | Article |
| id | doaj.art-38205e2a3af1456cacac988b48986f07 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-23T05:33:58Z |
| publishDate | 2012-03-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-38205e2a3af1456cacac988b48986f072022-12-21T17:58:23ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592012-03-018018Intersecting Quantum Gravity with Noncommutative Geometry - a ReviewJohannes AastrupJesper Møller GrimstrupWe review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holonomy loops. The spectral triple, which encodes the kinematics of quantum gravity, gives rise to a natural class of semiclassical states which entail emerging fermionic degrees of freedom. In the particular semiclassical approximation where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. We end the paper with an extended outlook section.http://dx.doi.org/10.3842/SIGMA.2012.018quantum gravitynoncommutative geometrysemiclassical analysis |
| spellingShingle | Johannes Aastrup Jesper Møller Grimstrup Intersecting Quantum Gravity with Noncommutative Geometry - a Review Symmetry, Integrability and Geometry: Methods and Applications quantum gravity noncommutative geometry semiclassical analysis |
| title | Intersecting Quantum Gravity with Noncommutative Geometry - a Review |
| title_full | Intersecting Quantum Gravity with Noncommutative Geometry - a Review |
| title_fullStr | Intersecting Quantum Gravity with Noncommutative Geometry - a Review |
| title_full_unstemmed | Intersecting Quantum Gravity with Noncommutative Geometry - a Review |
| title_short | Intersecting Quantum Gravity with Noncommutative Geometry - a Review |
| title_sort | intersecting quantum gravity with noncommutative geometry a review |
| topic | quantum gravity noncommutative geometry semiclassical analysis |
| url | http://dx.doi.org/10.3842/SIGMA.2012.018 |
| work_keys_str_mv | AT johannesaastrup intersectingquantumgravitywithnoncommutativegeometryareview AT jespermøllergrimstrup intersectingquantumgravitywithnoncommutativegeometryareview |