arXiv subjects
Publications and source records attributed to F. Guerin.
A real-time path integral for ultrasoft QCD is formulated. It exhibits a Feynman's influence functional. The statistical properties of the theory and the gauge symmetry are explicit. The correspondence is established with the alternative version, where a noise term enters a transport equation.
A recently proposed generating functional allows the construction of the full set of n-point Green functions in QCD at high temperature and at distances larger than 1/gT. One may then learn how the system maintains its thermal equilibrium in the quantum field theory approach, i.e. which process compensates for the important dissipation due to collisions. This system may be characterized by quantities which have a classical limit. One finds that the fluctuations of the coloured field are not gaussian ones. A comparison is made with the semi-classical approach where a random noise is the source of fluctuations.
The effective amplitudes for gluon momentum p<<gT in hot QCD exhibit damping as a result of collisions. The whole set of n-point amplitudes is shown to be generated from one functional K(x,y;A), in addition to the induced current j(x;A).
The Keldysh three- and four-point functions are related to analytical continuations of the Imaginary Time amplitudes,in momentum space. The relation provides an interesting interpretation of the amplitudes that are specific to the Keldysh basis, and of the Ward Identities they satisfy in QED. The interpretation carries over to the (perturbative) non-equilibrium case.
An effective theory for the soft field modes in hot QCD has been obtained recently by integrating out the field modes of momenta of order T and g T. The mean hard particle distribution obeys a transport equation with a collision term. The scale that comes out for the soft field is g^2 T ln 1/g . N-gluon soft amplitudes are shown to be a sum of tree diagrams and to obey tree-like Ward identities. These effective amplitudes are used to compute the one-soft loop contribution to the gluon self-energy when the loop momentum is of order g^2 T ln 1/g. It allows to identify a new collision term which, when included into the transport equation, takes into account collisions with gluon exchange of order g^2 T ln 1/g. The infrared behaviour of the collision term exhibits a significant change.
A review of the properties of this alternate basis is presented. To appear in the proceedings of the 3rd Workshop on Thermal Field Theory, Banff, August 1993.
The general relationship between a Retarded-Advanced Green function of the Real Time formalism and analytical continuations of the Imaginary Time Amplitude is obtained via perturbation theory. A 4-point R-A function is, at most, a linear combination of three analytical continuations, and a 5-point R-A function of seven continuations. The R-A functions are written as the sum of one analytical continuation plus discontinuities across single momentum transfer variables. These discontinuities