2010/05/31 by F. A. CHISHTIE, F. A. Chishtie, T. Hanif +8
Physics and Astronomy · #Black Holes and Theoretical Physics #Neutrino Physics Research #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.1142/s0217751x10051098
published as Int.J.Mod.Phys.A25:5711-5729,2010 · 16 pages; added 2 figures and 2 tables; references revised
arxiv created 2010/09/01 · openalex publication_date 2010/12/17 · arxiv updated 2011/01/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
When one uses the Coleman–Weinberg renormalization condition, the effective potential V in the massless [Formula: see text] theory with O(N) symmetry is completely determined by the renormalization group functions. It has been shown how the (p + 1) order renormalization group function determine the sum of all the N p LL order contribution to V to all orders in the loop expansion. We discuss here how, in addition to fixing the N p LL contribution to V, the (p + 1) order renormalization group functions can also be used to determine portions of the N p+n LL contributions to V. When these contributions are summed to all orders, the singularity structure of V is altered. An alternate rearrangement of the contributions to V in powers of ln ϕ, when the extremum condition V′(ϕ = v) = 0 is combined with the renormalization group equation, show that either v = 0 or V is independent of ϕ. This conclusion is supported by showing the LL , …, N 4 LL contributions to V become progressively less dependent on ϕ.