Classical scattering matrix for hard and soft excitations in a plasma with non-abelian interaction

Yu. A. Markov ; M. A. Markova ; N. Yu. Markov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 3, Tome 240 (2025), pp. 29-38.

Résumé

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 $\mathcal{S}$-matrix is determined in the form of the most general integro-power series in asymptotic values of the normal bosonic variables $c^{a}_{\boldsymbol{k}}(t)$ and $c^{\ast a}_{\boldsymbol{k}}(t)$ describing the soft gluon excitations of the system and the color charge $\mathcal{Q}^{a}(t)$ of the hard particle at $t\rightarrow\infty$. The first nontrivial contribution to the given $\mathcal{S}$-matrix is obtained.

Détail

Keywords: Hamiltonian formalism, classical scattering matrix, non-Abelian plasma, plasmon, color-charged particle
Mots-clés : Lie–Poisson bracket

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