Poisson brackets

1. Apr 25, 2013

stefano colom

l know you can define poisson brackets between two analytic function in several variables f(q1,q2,q3,..,p1,p2,p3,..) and g (q1,q2,q3,..,p1,p2,p3,..) only by foundamental poisson brackets and their proprieties.how is it possible?

Last edited: Apr 25, 2013
2. Apr 25, 2013

Jano L.

If the function is analytic, this means it is equal to its power expansion. If you substitute this Taylor expansion in the Poisson bracket you want to calculate, you can then use simple rules to simplify it (like P.B. of sum is sum of P.B. etc) to few basic P.B.s, like that for q1,p1.

3. Apr 26, 2013

stefano colom

how it is the power expansion of the function f(x,y)?
l know the power expansion of f(x), but the one of f(x,y)? can anyone tell me a website where l can find more informations about that?thank you

4. Apr 26, 2013

Jano L.

5. Apr 26, 2013

stefano colom

can you suggest me a site where l can find how to use taylor series with Poisson Brackets?

6. Apr 26, 2013

Jano L.

Unfortunatly I do not know any reference for this topic.