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Dynamics of wave fluctuations in the homogeneous Yang-Mills condensate

In the present work, the Yang-Mills (YM) quantum-wave excitations of the classical homogeneous YM condensate have been studied in quasi-classical approximation. The formalism is initially formulated in the Hamilton gauge and is based upon canonical quantisation in the Heisenberg representation. This canonical framework is then extended and related to YM dynamics in arbitrary gauge and symmetry group containing at least one $SU(2)$ subgroup. Such generic properties of the interacting YM system as excitation of longitudinal wave modes and energy balance between the evolving YM condensate and waves have been established. In order to prove these findings, the canonical quasi-classical YM system "waves + condensate" in the pure simplest $SU(2)$ gauge theory has been thoroughly analysed numerically in the linear and next-to-linear approximations in the limit of small wave amplitudes. The effective gluon mass dynamically generated by wave self-interactions in the gluon plasma has been derived. A complete set of equations of motion for the YM "condensate + waves" system accounting for second- and third-order interactions between the waves has been obtained. In the next-to-linear approximation in waves we have found that due to interactions between the YM waves and the YM condensate, the latter looses its energy leading to the growth of amplitudes of the YM wave modes. A similar effect has been found in the maximally-supersymmetric ${\cal N}=4$ Yang-Mills theory as well as in two-condensate $SU(4)$ model. Possible implications of these findings to Cosmology and gluon plasma physics have been discussed.