The Energy of the High-temperature Quark-gluon Plasma

For the quark-gluon plasma, an energy-momentum tensor is found corresponding to the high-temperature Braaten-Pisarski effective action. The tensor is found by considering the interaction of the plasma with a weak gravitational field and the positivity of the energy is studied. In addition, the complete effective action in curved spacetime is written down. 1 Introduction The high-temperature properties of the quark-gluon plasma are of some interest, both in their own right and as a starting point of a re-summation of perturbation theory [1]. These properties are encoded in an 'effective action' Γ, which has a coefficient proportional to T 2 (where T is the temperature) [2]. This effective action is nonlocal, but in a very special way. If Γ is taken rather literally as an action for an effective field theory, a question which comes to mind is: what is the associated energy-momentum tensor density T µν (x) and energy-momentum vector P µ ? Since Γ is nonlocal (in time as well as in space), the canonical construction for T µν is not available. An alternative definition of T µν is given as follows. First generalize Γ to a curved spacetime background (which is asymptotically Minkowskian), giving a functional ¯ Γ of the vierbein (e µa) and metric (as well as of the gluon and quark fields). Then