Finite-rank conformal quantum mechanics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916032384335872 |
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| author | Gritskov, Maxim Timchenko, Saveliy |
| author_facet | Gritskov, Maxim Timchenko, Saveliy |
| contents | In this work, we study the simplest example of the landscape of conformal field theories: one-dimensional CFTs with finite-dimensional state space. Following the definition of quantum field theory given by G. Segal, we formulate the condition under which a one-dimensional QFT (quantum mechanics) possesses conformal symmetry, and we give a complete classification of conformal Hamiltonians with finite rank. It turns out that correlation functions in such theories are polynomial functions of the underlying geometric data. Moreover, the one-dimensional conformal Ward identities determine their scaling behavior, so that the correlators of the conformal observables are, in fact, homogeneous polynomials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_06501 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite-rank conformal quantum mechanics Gritskov, Maxim Timchenko, Saveliy Mathematical Physics High Energy Physics - Theory In this work, we study the simplest example of the landscape of conformal field theories: one-dimensional CFTs with finite-dimensional state space. Following the definition of quantum field theory given by G. Segal, we formulate the condition under which a one-dimensional QFT (quantum mechanics) possesses conformal symmetry, and we give a complete classification of conformal Hamiltonians with finite rank. It turns out that correlation functions in such theories are polynomial functions of the underlying geometric data. Moreover, the one-dimensional conformal Ward identities determine their scaling behavior, so that the correlators of the conformal observables are, in fact, homogeneous polynomials. |
| title | Finite-rank conformal quantum mechanics |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.06501 |