Canonical transformation poisson bracket

1. What is Poisson bracket in canonical transformation?
2. What are the conditions for transformation to be canonical?
3. What does Poisson bracket represent?
4. What is canonical transformation explain?

What is Poisson bracket in canonical transformation?

Poisson Brackets under Canonical Transformations

with respect to a pair of variables p,q then those variables are said to be canonically conjugate. The Poisson bracket is invariant under a canonical transformation, meaning. [f,g]p,q=[f,g]P,Q.

What are the conditions for transformation to be canonical?

If λ = 1 then the transformation is canonical, which is what we will study. If λ = 1 then the transformation is extended canonical, and the results from λ = 1 can be recovered by rescaling q and p appropriately.

What does Poisson bracket represent?

The Poisson bracket in coordinate-free language

denotes the (entirely equivalent) Lie derivative of the function f. , it follows that every Hamiltonian vector field X_f is a symplectic vector field, and that the Hamiltonian flow consists of canonical transformations.

What is canonical transformation explain?

Example. A canonical transformation is often defined by saying that it must transform any Hamiltonian flow into another one, and this seems to be exactly the definition of a certain normalizer.