Light-front Hamiltonian for scalar field theories and the zero-mode problem

We determine matrix elements of the energy - momentum operator between light-front Fock states in a scalar field theory with a non-trivial vacuum expectation value of a field without the framework of the canonical light-front formalism. Special attention is given to the contribution of zero modes. To fix all the parameters entering such a light-front Hamiltonian, one is required to calculate the vacuum expectation values (VEV) for some products of fields at the same point. We discuss a method for calculation of such VEVs in the framework of the light-front Hamiltonian approach. We suggest that the solution of field theoretical models in the light-front Hamiltonian approach needs a self-consistent simultaneous determination both of the spectrum of and these VEVs. A self-consistency condition is considered.