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http://doi.org/10.25358/openscience-6392Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Becker, Maximilian | - |
| dc.date.accessioned | 2021-10-19T12:34:45Z | - |
| dc.date.available | 2021-10-19T12:34:45Z | - |
| dc.date.issued | 2021 | - |
| dc.identifier.uri | https://openscience.ub.uni-mainz.de/handle/20.500.12030/6402 | - |
| dc.description.abstract | The construction of a theory of quantum gravity is among the most challenging pursuits of modern-day physics. From the theoretician's point of view, there are some broad features that any theory of quantum gravity should exhibit. These include renormalizability, unitarity and Background Independence. However, because of the scarce experimental data available on the nature of the gravitational interaction at high energies, the specific realization of these requirements is rather unclear. Therefore, it is inevitable toincrease the variety of theoretical approaches towards quantum gravity. These can be parted into two main categories: Those that employ discrete structures at the fundamental level, such as Loop Quantum Gravity or Causal Dynamical Triangulations, and the continuum-based approaches such as the Asymptotic Safety scenario based upon the Effective Average Action, where the ultraviolet completion of quantum gravity is realized via a non-trivial fixed point of the renormalization group flow. Although each of these approaches' physical properties have been explored to some extent, still only little is known about their relationship to each other. A contact point that seems natural is the comparison of their geometric features at high energies. In the first part of this thesis, we derive suitable geometric features for the continuum-based approaches. Based on the functional renormalization group equation for gravity, we derive a novel flow equation that governs the evolution of renormalized composite operators. This evolution becomes encoded into that of the composite operators' anomalous dimensions. We show that their values in the fixed-point regime can be interpreted as quantum corrections to the classical scaling dimensions of the composite operators. As a main application, we calculate for the first time the scaling dimension at the ultraviolet fixed point of the volume operator for submanifolds embedded into spacetime, within the Einstein-Hilbert truncation as well as the truncation corresponding to higher-derivative gravity at one loop. In the former case, we observe dimensional reduction phenomena: The scaling dimension in the ultraviolet becomes much smaller than its classical value. This unveils the genuinely fractal nature of spacetime, and subsets of it, in the ultraviolet. In the latter case, we find that precisely at the ultraviolet fixed point the quantum corrections to the scaling dimension vanish, because of the asymptotic freedom of higher-derivative gravity. However, its fractal nature still is unveiled slightly away from the fixed point, where we, depending on the dimension of the submanifold, find that the effective scaling dimension either increases or decreases. In the second part of this thesis, we propose a novel quantization scheme for fields in contact with dynamical gravity, including quantum gravity itself. This scheme is subject to three essential requirements: Background Independence, the use of gravity-coupled approximants, and N-type cutoffs. Therewith we require that Background Independence is already implemented at the level of the regularized precursor of a quantum field theory, i.e., its "approximants". We realize this via the employment of cutoffs of the N-type, which constitute a metric-independent regularization scheme. We initiate the exploration of this quantization scheme by applying it to a scalar field in classical spacetimes, and then to quantum gravity itself, and determining the possible self-consistent spherical background geometries. These turn out to possess striking physical properties. In particular, they embody a solution to the notorious cosmological constant problem which, in the traditional approaches, arises due to the field's quantum vacuum fluctuations. | en_GB |
| dc.language.iso | eng | de |
| dc.rights | CC BY-ND | * |
| dc.rights.uri | https://creativecommons.org/licenses/by-nd/4.0/ | * |
| dc.subject.ddc | 530 Physik | de_DE |
| dc.subject.ddc | 530 Physics | en_GB |
| dc.title | The Renormalization of Geometric Operators and Background Independent Field Quantization in Quantum Gravity | en_GB |
| dc.type | Dissertation | de |
| dc.identifier.urn | urn:nbn:de:hebis:77-openscience-fc042e0d-8738-4903-80e7-df48606b9ab45 | - |
| dc.identifier.doi | http://doi.org/10.25358/openscience-6392 | - |
| jgu.type.dinitype | doctoralThesis | en_GB |
| jgu.type.version | Original work | de |
| jgu.type.resource | Text | de |
| jgu.date.accepted | 2021-10-01 | - |
| jgu.description.extent | xii, 407 Seiten | de |
| jgu.organisation.department | FB 08 Physik, Mathematik u. Informatik | de |
| jgu.organisation.year | 2020 | - |
| jgu.organisation.number | 7940 | - |
| jgu.organisation.name | Johannes Gutenberg-Universität Mainz | - |
| jgu.rights.accessrights | openAccess | - |
| jgu.organisation.place | Mainz | - |
| jgu.subject.ddccode | 530 | de |
| jgu.organisation.ror | https://ror.org/023b0x485 | |
| Appears in collections: | JGU-Publikationen | |
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| File | Description | Size | Format | ||
|---|---|---|---|---|---|
 | becker_maximilian-the_renormaliz-20211012145103183.pdf | 3.71 MB | Adobe PDF | View/Open |