Body fixed frame,rigid gauge rotations and largeN random fields in QCD

The body fixed frame with respect to local gauge transformations is introduced. Rigid gauge rotations in QCD and their Schrödinger equation are studied for static and dynamic quarks. Possible choices of the rigid gauge field configuration corresponding to a nonvanishing static colormagnetic field in the body fixed frame are discussed. A gauge invariant variational equation is derived in this frame. For large numberN of colors the rigid gauge field configuration is regarded as random with maximally random probability distribution under constraints on macroiscopic-like quantities. For the uniform magnetic field the joint probability distribution of the field components is determined by maximizing the appropriate entropy under the area law constraint for the Wilson loop. In the quark sector the gauge invariance requires the rigid gauge field configuration to appear not only as a background but also as inducing an instantaneous quark-quark interaction. Both are random in the largeN limit.Communicated by F. Lenz