Defining Poisson Brackets: Analytic Functions in Multiple Variables

[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?

 

[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.

 

[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

 

[Jano L.]

Search for "calculus of several/many variables". There is short section "Taylor series in several variables" on the wiki page:

http://en.wikipedia.org/wiki/Taylor_expansion

 

[stefano colom]

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

 

[Jano L.]

Unfortunatly I do not know any reference for this topic.