Canonical transformations as a category


by espen180
Tags: canonical, category, transformations
espen180
espen180 is offline
#1
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?
Phys.Org News Partner Physics news on Phys.org
Physicists design quantum switches which can be activated by single photons
'Dressed' laser aimed at clouds may be key to inducing rain, lightning
Higher-order nonlinear optical processes observed using the SACLA X-ray free-electron laser

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