Finiteness Conditions for Light-Front Hamiltonians

Many advantages of the light-front (LF) formulation for bound state problems arise from the manifest boost invariance in the longitudinal direction [1{5]. The price for this advantage is that other symmetries, such as parity or rotational invariance (for rotations around a transverse axis) are no longer manifest [6,7]. From the technical point of view, the loss of manifest parity and full rotational invariance implies that LF Hamiltonians allow for a richer set of counter-terms in the renormalization procedure, i.e. in general LF Hamiltonians contain more parameters than the underlying Lagrangian. Of course, even though parity and full rotational invariance are not manifest symmetries in the LF formulation, a consistent calculation should still give rise to physical observables which are consistent with these symmetries. In Ref. [7] this fact has been used to determine one of these additional parameters by imposing parity covariance on the vector form factor of mesons. While such a procedure is practical, it is nevertheless desirable to have alternative procedures available for determining these \additional" parameters in the Hamiltonian. In this paper, niteness conditions are exploited to develop algorithms for determining seemingly independent parameters in LF Hamiltonians. As a speci c example, let us consider a Yukawa model in 1+1 dimensions