# 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?

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted