Light-cone Hamiltonian ($H=(p_i^2+{\mu }^2)/(2p^{+})$)

With $d{s}^2=-2d{x}^{+}d{x}^{-}+d{x}_i^2$, $x^{+}=t$, and $p_{-}\ne 0$, the mass-shell condition gives $H=-p_{+}=-(p_i^2+{\mu }^2)/(2p_{-})$. In the future-directed sector $p^{+}=-p_{-}>0$, this is $(p_i^2+{\mu }^2)/(2p^{+})$. Its Schrodinger equation is equivalent to the Klein-Gordon equation after multiplication by $2p_{-}$.