Contrasting real-time dynamics with screening phenomena at finite temperature.

We discuss the interpretation of Euclidean correlation functions at finite temperature (T) and their relationship with the corresponding real-time Green’s functions. The soluble 2+1 dimensional Gross-Neveu model in the large-N limit is used throughout as a working example. First, the real-time bound state, identified as an elementary excitation at finite T, is solved. The bound state mass, the dispersion relation at low momenta, the coupling constant and decay constant are calculated. To characterize the structure of the bound state the on-shell form factor is carefully introduced and calculated. Then we examine the corresponding screening state and contrast the screening mass, coupling constant, decay constant and the screening Bethe-Salpeter amplitude with the real-time quantities. We find that, although they can be used as qualitative indicators in the low-T regime, the screening states at finite T in general do not reflect the properties of the corresponding real-time bound states. Besides, other relevant issues, such as the subtlety of the real-time manifestation of conservation laws due to some internal symmetries at T 6 0, the temperature dependence of the pseudoscalar spectral function and its sum rule, and the high-T limit of the screening state and its implications to the dimensional reduction, are also discussed in detail.