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A rigorous three-dimensional relativistic equation for quark-antiquark boundstates at finite temperature is derived from the thermal QCD generatingfunctional which is formulated in the coherent-state representation. Thegenerating functional is derived newly and given a correct path-integralexpression. The perturbative expansion of the generating functional isspecifically given by means of the stationary-phase method. Especially, theinteraction kernel in the three-dimensional equation is derived by virtue ofthe equations of motion satisfied by some quark-antiquark Green functions andgiven in a closed form which is expressed in terms of only a few types of Greenfunctions. This kernel is much suitable to use for exploring the deconfinementof quarks. To demonstrate the applicability of the equation derived, theone-gluon exchange kernel is derived and described in detail

european physical journal. c, particles and fields

Rigorous relativistic equation for quark–antiquark bound states at finite temperature derived from thermal QCD formulated in the coherent-state representation