Fluid-electromagnetic helicities and knotted solutions of the fluid-electromagnetic equations
In this paper we consider an Euler fluid coupled to external electromagnetism. We prove that the Hopfion fluid-electromagnetic knot, carrying fluid and electromagnetic (EM) helicities, solves the fluid dynamical equations as well as the Abanov Wiegmann (AW) equations for helicities, which are inspir...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2022 |
| Country: | Brasil |
| Institution: | Universidade Estadual Paulista (UNESP) |
| Repository: | Repositório Institucional da UNESP |
| Language: | English |
| OAI Identifier: | oai:repositorio.unesp.br:11449/248107 |
| Online Access: | http://dx.doi.org/10.1007/JHEP12(2022)144 http://hdl.handle.net/11449/248107 |
| Access Level: | Open access |
| Keyword: | Field Theory Hydrodynamics Solitons Monopoles and Instantons |
| Summary: | In this paper we consider an Euler fluid coupled to external electromagnetism. We prove that the Hopfion fluid-electromagnetic knot, carrying fluid and electromagnetic (EM) helicities, solves the fluid dynamical equations as well as the Abanov Wiegmann (AW) equations for helicities, which are inspired by the axial-current anomaly of a Dirac fermion. We also find a nontrivial knot solution with truly interacting fluid and electromagnetic fields. The key ingredients of these phenomena are the EM and fluid helicities. An EM dual system, with a magnetically charged fluid, is proposed and the analogs of the AW equations are written down. We consider a fluid coupled to a nonlinear generalizations for electromagnetism. The Hopfions are shown to be solutions of the generalized equations. We write down the formalism of fluids in 2+1 dimensions, and we dimensionally reduce the 3+1 dimensional solutions. We determine the EM knotted solutions, from which we derive the fluid knots, by applying special conformal transformations with imaginary parameters on un-knotted null constant EM fields. |
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