GAUGE INVARIANT CHROMOELECTROMAGNETIC FIELD AND HOT GLUON PLASMA-OSCILLATIONS

A gauge invariant description of the chromoelectromagnetic field and c olour current demands the use of nonlocal operators. We show that such operators can be constructed in a essentially unique way by enforcing full Poincare covariance, and that they are related through Maxwell, rather than Yang-Mills, equations. Their nonlocality entails the fact that causal and time-ordered propagators are no more the same object a nd, consequently, the relations between causal and retarded propagator s, which in the case of local fields are derived by means of Lehman re presentation, break down. The linear response theory approach to the p ropagation of long wavelength oscillations in hot gluon plasma is then reconsidered in the light of the above circumstance. We obtain manife stly gauge invariant plasmon frequency and decay width by computing th e retarded current-current commutator from its very definition in the real time formalism. In addition to finding the commonly accepted 1-lo op value for the plasma frequency and a positive 1-loop value for the Landau damping, we are able to give a non-perturbative proof of the po sitivity of the decay width, regardless of the high temperature expans ion. We finally discuss the coexistence of a positive plasmon width an d ultraviolet asymptotic freedom.