Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-05-11
Int.J.Mod.Phys.A25:5711-5729,2010
Physics
High Energy Physics
High Energy Physics - Theory
16 pages; added 2 figures and 2 tables; references revised
Scientific paper
10.1142/S0217751X10051098
When one uses the Coleman-Weinberg renormalization condition, the effective potential $V$ in the massless $\phi_4^4$ 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$^{\mbox{\scriptsize p}}$LL order contribution to $V$ to all orders in the loop expansion. We discuss here how, in addition to fixing the N$^{\mbox{\scriptsize p}}$LL contribution to $V$, the $(p+1)$ order renormalization group functions also can be used to determine portions of the N$^{\mbox{\scriptsize p+n}}$LL contributions to $V$. When these contributions are summed to all orders, the singularity structure of \mcv is altered. An alternate rearrangement of the contributions to $V$ in powers of $\ln \phi$, when the extremum condition $V^\prime (\phi = v) = 0$ is combined with the renormalization group equation, show that either $v = 0$ or $V$ is independent of $\phi$. This conclusion is supported by showing the LL, $\cdots$, N$^4$LL contributions to $V$ become progressively less dependent on $\phi$.
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Chishtie Farrukh A.
Hanif T.
Jia Junji
McKeon Dennis G. C.
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