
#1
Mar2812, 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? 


Register to reply 
Related Discussions  
What is the difference between canonical transformations and gauge transformations?  Classical Physics  1  
Canonical transformations  Classical Physics  11  
Classical canonical transformations and unitary transformations in quantum mechanics  Quantum Physics  21  
canonical transformations  Classical Physics  5  
Canonical Transformations  Advanced Physics Homework  2 