Dynamical symmetries of supersymmetric oscillators
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910535703855104 |
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| author | Sinha, Akash Ghosh, Aritra Bagchi, Bijan |
| author_facet | Sinha, Akash Ghosh, Aritra Bagchi, Bijan |
| contents | In this paper, we describe the dynamical symmetries of classical supersymmetric oscillators in one and two spatial (bosonic) dimensions. Our main ingredient is a generalized Poisson bracket which is defined as a suitable classical counterpart to commutators and anticommutators. In one dimension, i.e., in the presence of one bosonic and one fermionic coordinate, the Hamiltonian admits a $U(1,1)$ symmetry for which we explicitly compute the first integrals. It is found that suitable forms of the supercharges emerge in a natural way as fermionic conserved quantities. Following this, we describe classical supercharge operators based on the generalized Poisson bracket and subsequently define supersymmetry transformations. We perform a straightforward generalization to two spatial dimensions where the Hamiltonian has an overall $U(2,2)$ symmetry. We comment on plausible supersymmetric generalizations of the Pais-Uhlenbeck and isotonic oscillators, and also present the possibility of defining a generalized Nambu bracket within the classical formalism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_04747 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamical symmetries of supersymmetric oscillators Sinha, Akash Ghosh, Aritra Bagchi, Bijan Mathematical Physics High Energy Physics - Theory Classical Physics In this paper, we describe the dynamical symmetries of classical supersymmetric oscillators in one and two spatial (bosonic) dimensions. Our main ingredient is a generalized Poisson bracket which is defined as a suitable classical counterpart to commutators and anticommutators. In one dimension, i.e., in the presence of one bosonic and one fermionic coordinate, the Hamiltonian admits a $U(1,1)$ symmetry for which we explicitly compute the first integrals. It is found that suitable forms of the supercharges emerge in a natural way as fermionic conserved quantities. Following this, we describe classical supercharge operators based on the generalized Poisson bracket and subsequently define supersymmetry transformations. We perform a straightforward generalization to two spatial dimensions where the Hamiltonian has an overall $U(2,2)$ symmetry. We comment on plausible supersymmetric generalizations of the Pais-Uhlenbeck and isotonic oscillators, and also present the possibility of defining a generalized Nambu bracket within the classical formalism. |
| title | Dynamical symmetries of supersymmetric oscillators |
| topic | Mathematical Physics High Energy Physics - Theory Classical Physics |
| url | https://arxiv.org/abs/2304.04747 |