Solving two-dimensional phi4 field (complex scalar) theory by discretized light-front quantization.

Abstract

The discretized light-front quantization method is applied to ${\ensuremath{\varphi}}^{4}$ field (complex scalar) theory in 1 + 1 dimensions. The interaction Hamiltonian is constructed in its normal-ordered form, and calculations are performed with and without finite-mass renormalization in the charge-0 sector of the field. It is found that, like real scalar theory, finite-mass renormalization prevents the phase transition by restricting the theory to the weak-coupling region. A comparison of the results with and without mass renormalization demonstrates the same estimate of the critical coupling for which the mass gap vanishes. The invariant mass of various states is calculated as a function of bare coupling. In the weak-coupling region where extrapolation to the continuum limit is easily found, there is evidence for scattering, but there is no two-particle bound state in agreement with the well-known result established for constructive quantum field theory. Also, no multiparticle bound states are found. The essential outcome is that the results valid for real-scalar theories are found to be valid for complex scalar theory also.