Original scientific paper
Existence theorems for the differential equation of two effective couplings
Wolfhart Zimmermann
; Max-Planck-Instltut fur Physik unfd Astrophysik - Wrener Heisenberg-Institut fur Physik - D-8000 Munich 40, West Germany
Abstract
For massless models of quantum field theory with two independent couplings in¬variance under the renormalization group implies an ordinary differential equation which relates the effective couplings β and λ. In lowest order it is assumed that the β-function of g2 has the form b g4 with b ≠ 0 while the β-function of λ is a general bilinear form in λ and g2. For the exact system the solutions of the differential equation are studied near the singular point λ = g = 0. All solutions λ (g2) are determined for which the ratio λ/g2 stays bounded in the limit g → 0. For small g an explicit form of the asymptotic behaviour is obtained in agreement with formal asymptotic expansions found previously.
Keywords
Hrčak ID:
329863
URI
Publication date:
6.8.1985.
Visits: 241 *