Solving two-dimensionalφ4theory by discretized light-front quantization

The recently proposed discretized light-front quantization (DLFQ) method is applied to ${\phi }^4$ field theory in 1+1 dimensions. We start with the normal-ordered Hamiltonian and perform calculations with and without finite-mass renormalization in order to elucidate its role. We find that finite-mass renormalization prevents the phase transition by restricting the theory to the weak-coupling region. Comparison with results obtained without mass renormalization demonstrates that both treatments can yield the same estimate of the critical coupling for which the mass gap vanishes. This DLFQ estimate of the critical coupling may be compared with other estimates. The invariant mass of various states is calculated as a function of bare coupling. In the weak-coupling region where we can easily extrapolate to the continuum limit we find evidence for scattering but there is no two-particle bound state in agreement with the well-known result established for constructive quantum field theory. In addition, we find no multiparticle bound states.