Coordinate formalism on Hilbert manifolds

Details Coordinate formalism on Hilbert manifolds Coordinate formalism on Hilbert manifolds

2002-01-08

arxiv.org/abs/math-ph/0201017v1

Physics

Mathematical Physics

15 pages

Scientific paper

Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and infinite-dimensional manifolds deeply similar. In this context the obtained infinite-dimensional counterparts of simple notions such as basis, dual basis, orthogonal basis, etc. are shown to be closely related to the choice of a model. It is also shown that in this formalism a single tensor equation on an infinite-dimensional manifold produces a family of functional equations on different spaces of functions.

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