Hamiltonian formulation of the supersymmetric KdV equation
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910202143440896 |
|---|---|
| author | Pazarci, Ali Ghazanfari, Nadir Gahramanov, Ilmar |
| author_facet | Pazarci, Ali Ghazanfari, Nadir Gahramanov, Ilmar |
| contents | We studied the constrained Hamiltonian formulation of a supersymmetric Korteweg-de Vries (KdV) equation, which is observed to be a constrained system similar to its classical version. We found a nontrivial Lagrangian description, where we select $a=2$ for the free parameter $a$ in the supersymmetric extension. The corresponding degenerate Lagrangian requires an exclusive consideration and the utilization of the Dirac-Bergmann algorithm. We explicitly determined the full set of primary and secondary constraints and constructed the total Hamiltonian governing the dynamics of the system. In this analysis, in addition to a nontrivial constraint involving the fermionic fields, the consistency conditions give rise to a nonlocal contribution to the Hamiltonian density. This highlights a distinctive feature of this supersymmetric extension. We showed that the resulting Hamilton equations of motion reproduce the supersymmetric KdV system in the component form. Finally, we derived a compact superspace representation of the Hamiltonian and demonstrated its consistency with the component-level formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08065 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hamiltonian formulation of the supersymmetric KdV equation Pazarci, Ali Ghazanfari, Nadir Gahramanov, Ilmar Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems We studied the constrained Hamiltonian formulation of a supersymmetric Korteweg-de Vries (KdV) equation, which is observed to be a constrained system similar to its classical version. We found a nontrivial Lagrangian description, where we select $a=2$ for the free parameter $a$ in the supersymmetric extension. The corresponding degenerate Lagrangian requires an exclusive consideration and the utilization of the Dirac-Bergmann algorithm. We explicitly determined the full set of primary and secondary constraints and constructed the total Hamiltonian governing the dynamics of the system. In this analysis, in addition to a nontrivial constraint involving the fermionic fields, the consistency conditions give rise to a nonlocal contribution to the Hamiltonian density. This highlights a distinctive feature of this supersymmetric extension. We showed that the resulting Hamilton equations of motion reproduce the supersymmetric KdV system in the component form. Finally, we derived a compact superspace representation of the Hamiltonian and demonstrated its consistency with the component-level formulation. |
| title | Hamiltonian formulation of the supersymmetric KdV equation |
| topic | Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2605.08065 |