Abstract
In the present work, the Yang-Mills (YM) quantum-wave excitations of the classical homogeneous YM 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 and have been established. In order to prove these findings, the canonical quasi-classical YM system + 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 has been obtained. In the next-to-linear approximation in we have found that due to interactions between the YM 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 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. (Less)
Highlights
A consistent dynamical theory of the non-perturbative Yang-Mills (YM) vacuum, responsible e.g. for the spontaneous chiral symmetry breaking and color confinement phenomena in quantum chromodynamics (QCD) [1,2,3,4], has not yet been created
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
The N = 4 supersymmetric YM (SYM) theory includes four different fermion fields, three scalar and pseudo-scalar fields. Both numerically and analytically, that interactions of supersymmetric wave modes with the YM condensate lead to a similar energy swap effect from the YM condensate to thescalar wave modes as it was earlier observed for the vector wave modes in SU(2) gauge theory
Summary
A consistent dynamical theory of the non-perturbative Yang-Mills (YM) vacuum, responsible e.g. for the spontaneous chiral symmetry breaking and color confinement phenomena in quantum chromodynamics (QCD) [1,2,3,4], has not yet been created. It turned out that an inclusion of the vacuum polarisation effects dramatically change the time dependence of the YM condensate and its energy density — the latter becomes stationary in time and emerges as an extra constant (positive) contribution to the Lorentz-invariant Λ-term (i.e. satisfies to the vacuum equation of state p = −ε) the condensate U by itself is non-stationary which is an instanton-type solution (This is due to the fact that the equations of motion for the free condensate are not form-invariant under small quantum fluctuations.) So, the Lorentz-invariance of the energy-momentum tensor of such a quasi-free condensate U (t) is restored by the vacuum polarisation effects For this very first study, the latter argument motivates our simplest choice of initially free Lorentz non-invariant YM condensate (with no vacuum polarisation incorporated) which is spatially-homogeneous and isotropic. Canonical quantisation of the YM wave modes in the classical YM condensate has been performed in appendix B as a consistency check of the quasi-classical framework developed in this work
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