Definition:Hamiltonian

Definition
Let $J \sqbrk {\dotsm y_i \dotsm}$ be a functional of the form:


 * $\displaystyle J \sqbrk {\dotsm y_i \dotsm} = \intlimits {\int_{x_0}^{x_1} \map F {x, \cdots y_i \dotsm, \dotsm y_i \dotsm} \rd x} {i = 1} {i = n}$

Then the Hamilonian $H$ corresponding to $J \sqbrk {\dotsm y_i \dotsm}$ is defined as


 * $\displaystyle H = -F + \sum_{i \mathop = 1}^n y_i' F_{y_i'}$