Lie derivative clarification

redrzewski

I'm working thru Thirring's Classical Mathematical Physics. The lie derivative is defined and used on a vector field. I.e. L(x)f where x is a vector field. () = subscript

However, later on, he uses the lie derivative of the hamiltonian, which is a scalar function. I.e. L(H)f () = subscript

I'm assuming that this means the vector field induced by the hamiltonian, and not the lie derivative in the direction of the hamiltonian itself. However, usually Thirring is careful to call out this distinction (i.e. notating X(H) as the vector field induced by the hamiltonian).

My question: is it possible to have a lie derivative in the direction of a scalar function?

thanks

Related Differential Geometry News on Phys.org

Ben Niehoff

Gold Member
No, you can only take Lie derivatives with respect to a vector.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving