Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Summing Radiative Corrections to the Effective Potential   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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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat