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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.03030 |
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| _version_ | 1866912744017494016 |
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| author | Alonso-Monsalve, Elba |
| author_facet | Alonso-Monsalve, Elba |
| contents | When the gauge group of a theory has infinite volume, defining the inner product on physical states becomes subtle. This is the case for gravity, even in exactly solvable models such as minisuperspace or low-dimensional theories: the physical states do not inherit an inner product in a straightforward manner, and different quantization procedures yield a priori inequivalent prescriptions. This is one of the main challenges when constructing gravitational Hilbert spaces. In this paper we study a quantization procedure known as group averaging, which is a special case of the BRST/BV formalism and has gained popularity as a promising connection between Dirac quantization and gravitational path integrals. We identify a large class of theories for which group averaging is ill-defined due to isometry groups with infinite volume, which includes Jackiw-Teitelboim gravity. We propose a modification of group averaging to renormalize these infinite volumes and use it to quantize Jackiw-Teitelboim gravity with a positive cosmological constant in closed universes. The resulting Hilbert space naturally splits into infinite-dimensional superselection sectors and has a positive-definite inner product. This is the first complete Dirac quantization of this theory, as we are able to capture all the physical states for the first time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03030 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Hilbert space of gauge theories: group averaging and the quantization of Jackiw-Teitelboim gravity Alonso-Monsalve, Elba High Energy Physics - Theory When the gauge group of a theory has infinite volume, defining the inner product on physical states becomes subtle. This is the case for gravity, even in exactly solvable models such as minisuperspace or low-dimensional theories: the physical states do not inherit an inner product in a straightforward manner, and different quantization procedures yield a priori inequivalent prescriptions. This is one of the main challenges when constructing gravitational Hilbert spaces. In this paper we study a quantization procedure known as group averaging, which is a special case of the BRST/BV formalism and has gained popularity as a promising connection between Dirac quantization and gravitational path integrals. We identify a large class of theories for which group averaging is ill-defined due to isometry groups with infinite volume, which includes Jackiw-Teitelboim gravity. We propose a modification of group averaging to renormalize these infinite volumes and use it to quantize Jackiw-Teitelboim gravity with a positive cosmological constant in closed universes. The resulting Hilbert space naturally splits into infinite-dimensional superselection sectors and has a positive-definite inner product. This is the first complete Dirac quantization of this theory, as we are able to capture all the physical states for the first time. |
| title | The Hilbert space of gauge theories: group averaging and the quantization of Jackiw-Teitelboim gravity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.03030 |