The definition of a Legendre transformation given on the Wikipedia page http://en.wikipedia.org/wiki/Legendre_transformation is: given a function f(x), the Legendre transform f*(p) is(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f^*(p)=\max_x\left(xp-f(x)\right)[/tex]

Two questions: what does [tex]\max_x[/tex] mean here? And why is it not (explicitly?) included in the definition of the Hamiltonian

[tex]H(q,p)=p\dot{q}-L(q,\dot{q})[/tex]

if the Hamiltonian is a Legendre transformation?

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# Hamiltonian as Legendre transformation?

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