Science > Physics > Invariance As Part of Intersection Theory 7: Lagrangian Intersections/Submanifolds
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Science > Physics |
| User: |
"OsherD" |
| Date: |
07 Sep 2005 01:43:27 AM |
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Invariance As Part of Intersection Theory 7: Lagrangian Intersections/Submanifolds |
From Osher Doctorow
Lagrangian intersections and submanifolds are another branch of
Invariance-Intersection Theory which are currently being applied to
physics and have been for the last few years as exemplified by Front
For the Mathematics arXiv and also arXiv in the physics subcategory.
Readers might find it difficult to backtrack related definitions on the
internet, but PlanetMath.Org has a very clear definition of Lagrangian
Submanifold under those keywords as basically an isotropic
n-dimensional submanifold of a symplectic 2n-manifold. See also
http://planetmath.org/encyclopedia/LagrangianSubmanifold.html.
This n turns out to be the maximal dimension of isotropic submanifolds.
Physical applications range from classical Lagrangian and Hamiltonian
dynamics to coisotropc A-branes in the sigma model on a 4-torus to
dynamical systems and chaos and isolated conical singularities
including mirror symmetries and new invariants of Calabi-Yau 3-folds
usually on compact Riemannian m-manifolds, to boundary conformal field
theories and M5-branes and sigma models.
See hep-th/9906190, hep-th/0003242, math.DG/0211294 and /0211295,
math-ph/0505067 and math.DG/0505117 and hep-th/0501247 and
math.SG/0506016 v1 1 Jun 2005.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Invariance As Part of Intersection Theory 7: Lagrangian Intersections/Submanifolds |
07 Sep 2005 01:57:20 AM |
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From Osher Doctorow
It is somewhat interesting to note the wide variety of colleges of
researchers in Lagrangian submanifolds and intersections even among
those papers cited, including Oxford U. (Lincoln College), U. de Laguna
Canary Islands Spain, Penn State U., Northwestern U., plus Stanford (an
important paper not cited above). Perhaps the field is sufficiently
unexplored to prevent bureaucrats from noticing it and botching it and
de-emphasizing it, especially if they can't find even the definitions.
Osher Doctorow
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