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The dynamics of interacting particles is governed by a Hamiltonian
\[H = \sum_{i=1}^N\frac{|p_i|^2}{2m_i} + \frac{1}{2}
\sum_{i=1}^N\sum_{j=1}^N V_{ij}(\vec{r}_i-\vec{r}_j).\]
Suppose that we are viewing this system from a uniformly accelerating frame
\[\vec{r}^\prime_i = \vec{r}_i -\frac{1}{2} t^2.\]
Show that one can choose the canonical transformation connecting the to frames that is type 2 generating function \(F_2(\vec{r},\vec{p}^\prime,t)\) so that the Hamiltonian \(H^\prime\) in the accelerating frame has the same form as \(H\), except for an additional term which can be interpreted as arising out from the presence of an effective gravitational field \(-\vec{a}\). What is then the relation between the momenta \(\vec{p}_i\) and \(\vec{p}_i^\prime\) in the to frames?
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4727:Diamond Point
