THE LONG-RANGE INTERACTION IN MASSLESS (λΦ4)4 THEORY

Does massless (λΦ4)4 theory exhibit spontaneous symmetry breaking (SSB)? The raw one-loop result implies that it does, but the "RG-improved" result implies the opposite. We argue that the appropriate "low-energy effective theory" is a nonlocal field theory involving an attractive, long-range interaction Φ2(x)Φ2(y)/|x-y|4. RG improvement then requires running couplings for both this interaction and the original pointlike interaction. A crude calculation in this framework yields SSB even after "RG improvement" and closely agrees with the raw one-loop result.