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Canonical transformations as a category

by espen180
Tags: canonical, category, transformations
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Mar28-12, 05:13 AM
P: 836
I just realized that given a hamiltonian H, the set generated by its canonical transformations under composition just might be a category.

Just checking the axioms:
Given canonical transformations [itex]f:(H,q,p)\rightarrow (K,Q,P)[/itex] and [itex]g:(K,Q,P)\rightarrow (H^\prime, q^\prime,p^\prime)[/itex], [itex]g\circ f[/itex] is also canonical.

Also, the indentity transformation [itex]\text{id}:(H,q,p)\rightarrow (H,q,p)[/itex] exists and is canonical for any H, and associativity is trivially fulfilled. However, I cannot find any treatment of this category anywhere. It there simply no interest in it or anything to gain from this viewpoint?
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