Speaker
Description
We extend Noether’s first theorem to symmetries which are not symplectomorphisms but instead transform the symplectic form in a characteristic way. To do so, we use the framework of the covariant phase space method, and focus on the symmetries of the Euler-Lagrange equations which generalize the typical Lagrangian symmetries. We then show how under appropriate assumptions we can construct a dynamically conserved current and scalar charge from these general symmetries. Poisson-Lie symmetries (the semi-classical picture of quantum groups), provide a natural example of such generalized symmetries. We illustrate our framework with the generalized and deformed spinning top, the Klimcık-Severa non-linear σ-model, and 3D gravity as a BF theory, which all are shown to possess such Poisson-Lie type symmetries.
| Keywords | Quantum groups, symmetries, field theory, Poisson-Lie groups, quantum gravity |
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| Submitter's Email Address | [email protected] |
| Recording Permission | YES |
| Virtual Audience Permission | YES |
| Photography Permission | YES |
