Wigner functions in covariant and single-time formulations

Details Wigner functions in covariant and single-time formulations Wigner functions in covariant and single-time formulations

1998-06-15

arxiv.org/abs/hep-th/9806118v1

Annals Phys.266:351-416,1998

Physics

High Energy Physics

High Energy Physics - Theory

92 pages, to appear in Annals of Physics (N.Y.)

Scientific paper

10.1006/aphy.1998.5796

We will establish the connection between the Lorentz covariant and so-called single-time formulation for the quark Wigner operator. To this end we will discuss the initial value problem for the Wigner operator of a field theory and give a discussion of the gauge-covariant formulation for the Wigner operator including some new results concerning the chiral limit. We discuss the gradient or semi-classical expansion and the color and spinor decomposition of the equations of motion for the Wigner operator. The single-time formulation will be derived from the covariant formulation by taking energy moments of the equations for the Wigner operator. For external fields we prove that only the lowest energy moments of the quark Wigner operator contain dynamical information.

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