Register to reply

Canonical transformations as a category

by espen180
Tags: canonical, category, transformations
Share this thread:
espen180
#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
Physical constant is constant even in strong gravitational fields
Physicists provide new insights into the world of quantum materials
Nuclear spins control current in plastic LED: Step toward quantum computing, spintronic memory, better displays

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