Scale-dependent analysis of phase structures in quantum field theories

Abstract

The structure of the vacuum is studied in quantum field theories as a function of scale length R. As explicit examples, we analyze (1+1)-dimensional models which are exactly solvable in the leading 1/N approximation. In the Gross-Neveu model we find that chiral-symmetry breakdown occurs dynamically only at a long-distance scale (RR/sub c/); conversely, at a short-distance scale (R>R/sub c/) the gauge field is massive as a consequence of the symmetry breaking and does not produce a linear potential; R/sub c/ can be interpreted as the size of the bag within which quarks are confined. We also consider a modified Gross-Neveu model which has a permutation group S/sub L/ as an additional symmetry, where we analyze the dynamical breakdown of the S/sub L/ symmetry and the mass spectrum as a function of scale length R. In all these models the vacuum undergoes a phase transition in scale length R; for RR/sub c/ it is an ordered phase. It is emphasized that the critical point R/sub c/ is renormalization-group invariant.