Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization-group Calculation of Color-Coulomb Potential   We report here on the application of the perturbative renormalization-group
to the Coulomb gauge in QCD. We use it to determine the high-momentum
asymptotic form of the instantaneous color-Coulomb potential $V(\vec{k})$ and
of the vacuum polarization $P(\vec{k}, k_4)$. These quantities are
renormalization-group invariants, in the sense that they are independent of the
renormalization scheme. A scheme-independent definition of the running coupling
constant is provided by $\vec{k}^2 V(\vec{k}) = x_0
g^2(\vec{k}/\Lambda_{coul})$, and of $\alpha_s \equiv {{g^2(\vec{k} /
\Lambda_{coul})} \over {4\pi}}$, where $x_0 = {{12N} \over {11N - 2N_f}}$, and
$\Lambda_{coul}$ is a finite QCD mass scale. We also show how to calculate the
coefficients in the expansion of the invariant $\beta$-function $\beta(g)
\equiv |\vec{k}| {{\partial g} \over{\partial |\vec{k}|}} = -(b_0 g^3 + b_1 g^5
+b_2 g^7 + ...)$, where all coefficients are scheme-independent.

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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys