  We develop methods for computing the effective action at infinite momentum
for $1+1d$ QFTs at finite volume which do not rely on the theory having a
Lagrangian description. We do this by taking the infinite momentum limit of
equal-time quantization and integrating out all except for the chiral modes of
the theory. Our main application of this method is to the Ising Field Theory
(IFT), with an energy and magnetic deformation, where we compute the effective
lightcone Hamiltonian numerically and check it against results from TCSA.
Remarkably, in the low-temperature phase, the Lorentz invariant effective
Hamiltonian at infinite momentum takes a very compact form and depends on the
volume only through the finite volume vacuum expectation value of
$\langle\sigma\rangle$, the spin operator.
