I am reading a paper Okuguchi,1981 with a Ramsey growth model. There is a constant population growth $n$ such as $L(t)=e^{nt}$. The way he writes the Hamiltonian is quite interesting (equation 5 on page 658.)
$$H=e^{-(\rho+n\left(1-\sigma\right))t}\left[\frac{C^{1-\sigma}}{1-\sigma}+\psi AG+\phi\left(Q-C\right)\right]+\lambda R$$
where capital letters represent the aggregate variables and not per capita variables. $\lambda$ is constant in the model.
In fact, the author does not deal with per capita variables but aggregate variables. Of course, he takes into account the population growth since $n$ appears in co-state dynamics. However, I can not understand how he puts the exponential term $e^{-(\rho+n\left(1-\sigma\right))t}$ in the Hamiltonian in this way. I would really appreciate if you give me some hints or suggestions.
In the same fashion, is it correct to write something like
$$H=e^{-(\rho-n)t}\left[U\left(C\right)+\lambda\left(AK-C\right)+\mu\left(\left(1-S\right)S-\gamma AK\right)\right]$$