advanced_notions:chern-simons
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advanced_notions:chern-simons [2017/11/20 13:48] jakobadmin [Student] |
advanced_notions:chern-simons [2017/11/20 14:48] jakobadmin [Student] |
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| - | **In Fluid Mechanics:** | + | -->In Fluid Mechanics# |
| In the beginning people tried to make a mechanical model of electrodynamics. For example, Maxwell though of Faraday's electric and magnetic field lines as "fine tubes of variable section carrying an incompressible fluid". | In the beginning people tried to make a mechanical model of electrodynamics. For example, Maxwell though of Faraday's electric and magnetic field lines as "fine tubes of variable section carrying an incompressible fluid". | ||
| Line 81: | Line 81: | ||
| to twist is familiar to anyone seeking to | to twist is familiar to anyone seeking to | ||
| straighten out a coiled garden hose. | straighten out a coiled garden hose. | ||
| - | * [[http://www.pnas.org/content/111/10/3663.full.pdf|Helicity and singular structures in fluid dynamics]] by H. Keith Moffatt | + | |
| + | [[http://www.pnas.org/content/111/10/3663.full.pdf|Helicity and singular structures in fluid dynamics]] by H. Keith Moffatt | ||
| </blockquote> | </blockquote> | ||
| Line 104: | Line 105: | ||
| For more information on this obstruction to construct the Lagrangian for Euler's fluid equations, see page 9ff in https://arxiv.org/pdf/hep-th/0004084.pdf and the great review: | For more information on this obstruction to construct the Lagrangian for Euler's fluid equations, see page 9ff in https://arxiv.org/pdf/hep-th/0004084.pdf and the great review: | ||
| - | * [[http://www.annualreviews.org/doi/pdf/10.1146/annurev.fl.20.010188.001301|HAMILTONIAN FLUID MECHANICS]] by Rick Salmon | + | [[http://www.annualreviews.org/doi/pdf/10.1146/annurev.fl.20.010188.001301|HAMILTONIAN FLUID MECHANICS]] by Rick Salmon |
| - | **In Electrodynamics** | + | For an experimental proof that knotted vortices exist indeed in nature, see [[https://www.nature.com/articles/nphys2560|Creation and dynamics of knotted vortices]] by Dustin Kleckner & William T. M. Irvine |
| + | |||
| + | <-- | ||
| + | |||
| + | -->In Electrodynamics# | ||
| <blockquote>The magnetic helicity is the flux of the magnetic field through the surface bounding the volume, | <blockquote>The magnetic helicity is the flux of the magnetic field through the surface bounding the volume, | ||
| Line 137: | Line 142: | ||
| the fields themselves) thereby avoiding dissipation [1]. | the fields themselves) thereby avoiding dissipation [1]. | ||
| <cite>[[https://arxiv.org/pdf/hep-th/9911072.pdf|Creation and evolution of magnetic helicity]] by R. Jackiw et. al.</cite></blockquote> | <cite>[[https://arxiv.org/pdf/hep-th/9911072.pdf|Creation and evolution of magnetic helicity]] by R. Jackiw et. al.</cite></blockquote> | ||
| + | <-- | ||
| - | **In Non-Abelian Gauge Theories** | + | -->In Non-Abelian Gauge Theories# |
| "anomalous currents are sourced by gauge field configurations with nonzero Chern-Simons number. The | "anomalous currents are sourced by gauge field configurations with nonzero Chern-Simons number. The | ||
| Line 165: | Line 171: | ||
| Ref 21 is [[http://xxx.lanl.gov/abs/hep-th/9911072|Creation and evolution of magnetic helicity]] by R. Jackiw, So-Young Pi | Ref 21 is [[http://xxx.lanl.gov/abs/hep-th/9911072|Creation and evolution of magnetic helicity]] by R. Jackiw, So-Young Pi | ||
| + | |||
| + | <-- | ||
| <tabbox Researcher> | <tabbox Researcher> | ||
| <blockquote>On a manifold it is necessary to use covariant differentiation; curvature measures its noncommutativitiy. Its combination as a characteristic form measures the nontriviality of the underlying bundle. This train of ideas is so simple and natural that its importance can hardly be exaggerated. <cite>Shiing-shen Cern</cite></blockquote> | <blockquote>On a manifold it is necessary to use covariant differentiation; curvature measures its noncommutativitiy. Its combination as a characteristic form measures the nontriviality of the underlying bundle. This train of ideas is so simple and natural that its importance can hardly be exaggerated. <cite>Shiing-shen Cern</cite></blockquote> | ||
advanced_notions/chern-simons.txt · Last modified: 2017/11/22 10:46 by jakobadmin
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