Nonperturbative renormalization group in a light-front three-dimensional real scalar model

Abstract

The three-dimensional real scalar model, in which the $Z_2$ symmetry spontaneously breaks, is renormalized in a nonperturbative manner based on the Tamm-Dancoff truncation of the Fock space. A critical line is calculated by diagonalizing the Hamiltonian regularized with basis functions. The marginal (${\varphi }^6$) coupling dependence of the critical line is weak. In the broken phase the canonical Hamiltonian is tachyonic, so the field is shifted as $\varphi (x)\to \phi (x)+v$. The shifted value $v$ is determined as a function of running mass and coupling so that the mass of the ground state vanishes.

Comments: 23 pages, LaTeX, 6 Postscript figures, uses revTeX and epsbox.sty. A slight revision of statements made, some references added, typos corrected