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Results tagged with reference-request
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user 17047
This tag is used if a reference is needed in a paper or textbook on a specific result.
22
votes
Hamiltonian, Lagrangian and Newton formalism of mechanics
Each of the different formalism of classical mechanics has its advantages and disadvantages. However, in the end all three frameworks tend to be equivalent, and thus the following list is very subject …
- 5,824
11
votes
Hodge decomposition of smooth n-forms: is it an isomorphism of topological vector spaces?
Yes, the Hodge decomposition is a topological decomposition with respect to the $C^\infty$-topology. One can argue, for example, that the Laplace-Beltrami $\Delta$ operator is elliptic and hence can b …
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7
votes
1
answer
1k
views
Differential forms along the fiber
Let $E \to M$ be a smooth fiber bundle. Instead of differential forms defined on the whole tangent bundle $TE$ one could also consider forms on the vertical tangent bundle $VE$, i.e. forms defined on …
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7
votes
Accepted
General wedge-product for vector bundle valued forms
The most general definition I know is the following. Every fiberwise bilinear form $\eta: V_1 \times V_2 \to W$ of vector bundles $V_1, V_2, W$ over $M$ gives rise to the wedge product of vector-bundl …
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6
votes
Compressible Ebin-Marsden?
The compressible case uses semidirect products of groups (group of diffeomorphisms times functions).
To my knowledge, the first paper that discusses this in detail is
Marsden, Ratiu, Weinstein: Semidi …
- 5,824
5
votes
Accepted
Proof of the Hamiltonian slice theorem
The following textbooks contain a proof of the symplectic slice theorem:
Juan-Pablo Ortega and Tudor S. Ratiu: Momentum Maps and Hamiltonian Reduction
Gerd Rudolph and Matthias Schmidt: Differential …
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5
votes
Accepted
Quotient by freely acting group on Banach manifold
In finite dimensions, properness of the action is all you need for a slice theorem (and thus for the manifold structure of the quotient). However, in the Banach realm, properness is not enough. For ex …
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2
votes
Frechet Lie groups and their subgroups
Concerning your second point, it is no longer true that closed subgroups are Lie subgroups (even in the Hilbert setting). The corresponding result in infinite dimensions needs additional assumptions c …
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2
votes
1
answer
255
views
Parameter dependent differential equation in a Lie group
It is well-known that a linear differential equation in a finite-dimensional vector space depends continuously on some external parameters (for details see below). I search for an explicit reference w …
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1
vote
Local structure of the quotient of a Lie group action
If you know German, then I strongly recommend you the Habilitation thesis of Markus Pflaum: "Ein Beitrag zur Geometrie und Analysis auf stratifizierten Räumen" for the stratification of the orbit spa …
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1
vote
Quantization of a classical system (e.g. the case of a billiard)
As the non-uniques of a quantization scheme was already brought up, I will add a nice resource which gives a broad overview of different techniques:
Quantization Methods: A Guide for Physicists and A …
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