Hamiltonian Renormalization V: Free Vector Bosons
In a recent proposal we applied methods from constructive QFT to derive a Hamiltonian Renormalization Group in order to employ it ultimately for canonical quantum gravity. The proposal was successfully tested for free scalar fields and thus a natural next step is to test it for free gauge theories....
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2021-01-01
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| Series: | Frontiers in Astronomy and Space Sciences |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fspas.2020.547550/full |
| _version_ | 1819075674839711744 |
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| author | K. Liegener T. Thiemann |
| author_facet | K. Liegener T. Thiemann |
| author_sort | K. Liegener |
| collection | DOAJ |
| description | In a recent proposal we applied methods from constructive QFT to derive a Hamiltonian Renormalization Group in order to employ it ultimately for canonical quantum gravity. The proposal was successfully tested for free scalar fields and thus a natural next step is to test it for free gauge theories. This can be done in the framework of reduced phase space quantization which allows using techniques developed earlier for scalar field theories. In addition, in canonical quantum gravity one works in representations that support holonomy operators which are ill defined in the Fock representation of say Maxwell or Proca theory. Thus, we consider toy models that have both features, i.e. which employ Fock representations in which holonomy operators are well-defined. We adapt the coarse graining maps considered for scalar fields to those theories for free vector bosons. It turns out that the corresponding fixed pointed theories can be found analytically. |
| first_indexed | 2024-12-21T18:29:10Z |
| format | Article |
| id | doaj.art-18456ff0019743968a4c2c7de266eb45 |
| institution | Directory Open Access Journal |
| issn | 2296-987X |
| language | English |
| last_indexed | 2024-12-21T18:29:10Z |
| publishDate | 2021-01-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Astronomy and Space Sciences |
| spelling | doaj.art-18456ff0019743968a4c2c7de266eb452022-12-21T18:54:20ZengFrontiers Media S.A.Frontiers in Astronomy and Space Sciences2296-987X2021-01-01710.3389/fspas.2020.547550547550Hamiltonian Renormalization V: Free Vector BosonsK. Liegener0T. Thiemann1Institute for Theoretical Physics, University of Hamburg, Hamburg, GermanyInstitute for Quantum Gravity, FAU Erlangen–Nürnberg, Erlangen, GermanyIn a recent proposal we applied methods from constructive QFT to derive a Hamiltonian Renormalization Group in order to employ it ultimately for canonical quantum gravity. The proposal was successfully tested for free scalar fields and thus a natural next step is to test it for free gauge theories. This can be done in the framework of reduced phase space quantization which allows using techniques developed earlier for scalar field theories. In addition, in canonical quantum gravity one works in representations that support holonomy operators which are ill defined in the Fock representation of say Maxwell or Proca theory. Thus, we consider toy models that have both features, i.e. which employ Fock representations in which holonomy operators are well-defined. We adapt the coarse graining maps considered for scalar fields to those theories for free vector bosons. It turns out that the corresponding fixed pointed theories can be found analytically.https://www.frontiersin.org/articles/10.3389/fspas.2020.547550/fullrenormalization groupcanonical quantum gravityHamiltonian renormalizationconstructive QFTlattice gauge field theory |
| spellingShingle | K. Liegener T. Thiemann Hamiltonian Renormalization V: Free Vector Bosons Frontiers in Astronomy and Space Sciences renormalization group canonical quantum gravity Hamiltonian renormalization constructive QFT lattice gauge field theory |
| title | Hamiltonian Renormalization V: Free Vector Bosons |
| title_full | Hamiltonian Renormalization V: Free Vector Bosons |
| title_fullStr | Hamiltonian Renormalization V: Free Vector Bosons |
| title_full_unstemmed | Hamiltonian Renormalization V: Free Vector Bosons |
| title_short | Hamiltonian Renormalization V: Free Vector Bosons |
| title_sort | hamiltonian renormalization v free vector bosons |
| topic | renormalization group canonical quantum gravity Hamiltonian renormalization constructive QFT lattice gauge field theory |
| url | https://www.frontiersin.org/articles/10.3389/fspas.2020.547550/full |
| work_keys_str_mv | AT kliegener hamiltonianrenormalizationvfreevectorbosons AT tthiemann hamiltonianrenormalizationvfreevectorbosons |