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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2411.11078 |
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| _version_ | 1866910702451556352 |
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| author | Balachandran, A. P. |
| author_facet | Balachandran, A. P. |
| contents | The Palatini action is based on vector-valued one forms or frames and SL(2,C) connections on R^4. Using the spacetime split of R^4 as a direct sum of R^3 and R^1, the Gauss law in this paper is treated on a Hilbert space. This is achieved by noting that quantum operators act on a complex Hilbert space and SL(2,C) is just the complexification of the compact SU(2) in the self-dual (1/2,0) representation used for the Ashtekar variables. This observation enables a treatment of small and large gauge transformations and superselection sectors. An explicit representation of theta vacua and their attendant 'spin-isospin mixing' are also shown. It is argued that the Gauss law algebra replaces that of diffeomorphisms in the Palatini approach : operators implementing the latter with the correct algebraic relations do not seem available. (Those obtained by multiplying Gauss law operators with fields do not have the correct commutators.) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic Quantization of Palatini Action Balachandran, A. P. General Relativity and Quantum Cosmology High Energy Physics - Theory The Palatini action is based on vector-valued one forms or frames and SL(2,C) connections on R^4. Using the spacetime split of R^4 as a direct sum of R^3 and R^1, the Gauss law in this paper is treated on a Hilbert space. This is achieved by noting that quantum operators act on a complex Hilbert space and SL(2,C) is just the complexification of the compact SU(2) in the self-dual (1/2,0) representation used for the Ashtekar variables. This observation enables a treatment of small and large gauge transformations and superselection sectors. An explicit representation of theta vacua and their attendant 'spin-isospin mixing' are also shown. It is argued that the Gauss law algebra replaces that of diffeomorphisms in the Palatini approach : operators implementing the latter with the correct algebraic relations do not seem available. (Those obtained by multiplying Gauss law operators with fields do not have the correct commutators.) |
| title | Asymptotic Quantization of Palatini Action |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.11078 |