  We give an alternative derivation for the explicit formula of the effective
Hamiltonian describing the evolution of the quantum state of any number of
photons entering a linear optics multiport. The description is based on the
effective Hamiltonian of the optical system for a single photon and comes from
relating the evolution in the Lie group that describes the unitary evolution
matrices in the Hilbert space of the photon states to the evolution in the Lie
algebra of the Hamiltonians for one and multiple photons. We give a few
examples of how a group theory approach can shed light on some properties of
devices with two input ports.
