Gauged permutation invariant matrix quantum mechanics: Path Integrals
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909092349476864 |
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| author | O'Connor, Denjoe Ramgoolam, Sanjaye |
| author_facet | O'Connor, Denjoe Ramgoolam, Sanjaye |
| contents | We give a path integral construction of the quantum mechanical partition function for gauged finite groups. Our construction gives the quantization of a system of $d$, $N\times N$ matrices invariant under the adjoint action of the symmetric group $S_N$. The approach is general to any discrete group. For a system of harmonic oscillators, i.e. for the non-interacting case, the partition function is given by the Molien-Weyl formula times the zero-point energy contribution. We further generalise the result to a system of non-square and complex matrices transforming under arbitrary representations of the gauge group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12397 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gauged permutation invariant matrix quantum mechanics: Path Integrals O'Connor, Denjoe Ramgoolam, Sanjaye High Energy Physics - Theory We give a path integral construction of the quantum mechanical partition function for gauged finite groups. Our construction gives the quantization of a system of $d$, $N\times N$ matrices invariant under the adjoint action of the symmetric group $S_N$. The approach is general to any discrete group. For a system of harmonic oscillators, i.e. for the non-interacting case, the partition function is given by the Molien-Weyl formula times the zero-point energy contribution. We further generalise the result to a system of non-square and complex matrices transforming under arbitrary representations of the gauge group. |
| title | Gauged permutation invariant matrix quantum mechanics: Path Integrals |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.12397 |