Hamiltonian formalism for Bose excitations in a plasma with a non-Abelian interaction II: plasmon - hard particle scattering and energy loss

作     者：Markov, Yu.A. Markova, M.A. Markov, N.Yu. 

作者机构：Matrosov Institute for System Dynamics and Control Theory Siberian Branch Russian Academy of Sciences Irkutsk664033 Russia 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Hamiltonians 

摘      要：It is shown that the Hamiltonian formalism proposed previously in [1] to describe the nonlinear dynamics of only soft fermionic and bosonic excitations contains much more information than initially assumed. In this paper, we have demonstrated in detail that it also proved to be very appropriate and powerful in describing a wide range of other physical phenomena, including the scattering of colorless plasmons off hard thermal (or external) color-charged particles moving in hot quark-gluon plasma. A generalization of the Poisson superbracket including both anticommuting variables for hard modes and normal variables of the soft Bose field, is presented for the case of a continuous medium. The corresponding Hamilton equations are defined, and the most general form of the third- and fourth-order interaction Hamiltonians is written out in terms of the normal boson field variables and hard momentum modes of the quark-gluon plasma. The canonical transformations involving both bosonic and hard mode degrees of freedom of the system under consideration, are discussed. The canonicity conditions for these transformations based on the Poisson superbracket, are derived. The most general structure of canonical transformations in the form of integro-power series up to sixth order in a new normal field variable and a new hard mode variable, is presented. For the hard momentum mode of quark-gluon plasma excitations, an ansatz separating the color and momentum degrees of freedom, is proposed. The question of approximation of the total effective scattering amplitude when the momenta of hard excitations are much larger than those of soft excitations of the plasma, is considered. A detailed analysis of the connection between the approach presented in this paper and that proposed in our earlier work [2], is provided. An application of the developed Hamilton theory to the problem of calculating energy loss of an energetic color particle propagating through a hot QCD-medium, is considered. ©