<p>Within the framework of the Zakharov–Shulman approach, we determine the classical scattering matrix for the simplest process of interaction between hard and soft excitations in a quark-gluon plasma. Calculations are performed in close analogy with the methods of quantum field theory, with the replacement of the quantum commutator of quantum field operators by the so-called Lie–Poisson bracket of classical variables. The classical <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7947_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {S}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation>-matrix is determined in the form of the most general integro-power series in asymptotic values of the normal bosonic variables <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7947_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">$c^{a}_{\varvec{k}}(t)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>c</mi> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> <mi>a</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7947_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">$c^{*a}_{\varvec{k}}(t)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mi>c</mi> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> <mrow> <mrow /> <mo>∗</mo> <mi>a</mi> </mrow> </mmultiscripts> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> describing the soft gluon excitations of the system and the color charge <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7947_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {Q}^{a}(t)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="script">Q</mi> </mrow> <mi>a</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of the hard particle at <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7947_Article_IEq5.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">$t\rightarrow \infty $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo stretchy="false">→</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>. The first nontrivial contribution to the given <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7947_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {S}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation>-matrix is obtained.</p>

CLASSICAL SCATTERING MATRIX FOR HARD AND SOFT EXCITATIONS IN A PLASMA WITH NON-ABELIAN INTERACTION

期刊论文
发表日期：

2025年8月1日

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Yu. A. Markov,
M. A. Markova,
N. Yu. Markov

摘要

Within the framework of the Zakharov–Shulman approach, we determine the classical scattering matrix for the simplest process of interaction between hard and soft excitations in a quark-gluon plasma. Calculations are performed in close analogy with the methods of quantum field theory, with the replacement of the quantum commutator of quantum field operators by the so-called Lie–Poisson bracket of classical variables. The classical $\mathcal {S}$ $S$ -matrix is determined in the form of the most general integro-power series in asymptotic values of the normal bosonic variables $c^{a}_{\varvec{k}}(t)$ $c_{k}^{a} (t)$ and $c^{*a}_{\varvec{k}}(t)$ $c_{k}^{* a} (t)$ describing the soft gluon excitations of the system and the color charge $\mathcal {Q}^{a}(t)$ $Q^{a} (t)$ of the hard particle at $t\rightarrow \infty $ $t \to \infty$ . The first nontrivial contribution to the given $\mathcal {S}$ $S$ -matrix is obtained.