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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2501.16104 |
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| _version_ | 1866929688058789888 |
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| author | Gunneberg, Finlay Gratus, Jonathan Stanfield, Harvey |
| author_facet | Gunneberg, Finlay Gratus, Jonathan Stanfield, Harvey |
| contents | Plasma kinetics, for both flat and curved spacetime, is conventionally performed on the mass shell, a 7--dimensional time-phase space with a Vlasov vector field, also known as the Liouville vector field. The choice of this time-phase space encodes the parameterisation of the underling 2nd order ordinary differential equations. By replacing the Vlasov vector on time-phase space with a bivector on an 8--dimensional sub-bundle of the tangent bundle, we create a parameterisation free version of Vlasov theory. This has a number of advantages, which include working for lightlike and ultra-relativistic particles, non metric connections, and metric-free and premetric theories. It also works for theories where no time-phase space can exist for topological topological reasons. An example of this is when we wish to consider all geodesics, including spacelike geodesics.
We extend the particle density function to a 6--form on the subbundle of the tangent space, and define the transport equations, which correspond to the Vlasov equation. We then show how to define the corresponding 3--current on spacetime. We discuss the stress-energy tensor needed for the Einstein-Vlasov system.
This theory can be generalised to create parameterisation invariant Vlasov theories for many 2nd order theories, on arbitrary manifolds. The relationship to sprays and semi-sprays is given and examples from Finsler geometry are also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16104 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Vlasov Bivector: A Parameter-Free Approach to Vlasov Kinematics Gunneberg, Finlay Gratus, Jonathan Stanfield, Harvey Mathematical Physics High Energy Physics - Theory Plasma kinetics, for both flat and curved spacetime, is conventionally performed on the mass shell, a 7--dimensional time-phase space with a Vlasov vector field, also known as the Liouville vector field. The choice of this time-phase space encodes the parameterisation of the underling 2nd order ordinary differential equations. By replacing the Vlasov vector on time-phase space with a bivector on an 8--dimensional sub-bundle of the tangent bundle, we create a parameterisation free version of Vlasov theory. This has a number of advantages, which include working for lightlike and ultra-relativistic particles, non metric connections, and metric-free and premetric theories. It also works for theories where no time-phase space can exist for topological topological reasons. An example of this is when we wish to consider all geodesics, including spacelike geodesics. We extend the particle density function to a 6--form on the subbundle of the tangent space, and define the transport equations, which correspond to the Vlasov equation. We then show how to define the corresponding 3--current on spacetime. We discuss the stress-energy tensor needed for the Einstein-Vlasov system. This theory can be generalised to create parameterisation invariant Vlasov theories for many 2nd order theories, on arbitrary manifolds. The relationship to sprays and semi-sprays is given and examples from Finsler geometry are also given. |
| title | The Vlasov Bivector: A Parameter-Free Approach to Vlasov Kinematics |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2501.16104 |