# Canonical transformations as a category

1. Mar 28, 2012

### espen180

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 $f:(H,q,p)\rightarrow (K,Q,P)$ and $g:(K,Q,P)\rightarrow (H^\prime, q^\prime,p^\prime)$, $g\circ f$ is also canonical.

Also, the indentity transformation $\text{id}:(H,q,p)\rightarrow (H,q,p)$ 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?