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This pinch singularity is physical and reflects the absence of collisions (infinite time between scatterings) in the noninteracting theory. In kinetic theory within the relaxation time approximation, infinite scattering time means infinite relaxation time and therefore infinite viscosity 1. To obtain a finite viscosity, scattering processes must be taken into account. These give the plasma particles a non-zero collisional width which shifts the poles of the single particle propagator away from the real axis, thereby regulating the pinch singularity and rendering the limits of zero momentum and energy in Eqs. (2) and (12) well defined and independent of the order in which they are taken. Following Jeon 35 we account for this need for a finite collisional width by organizing the calculation in terms of skeleton diagrams involving full propagators. Extracting the leading order contribution to the viscosity then amounts to specifying for each line in the skeleton diagram individually the required accuracy for the single particle self-energy in powers of the coupling constant
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This pinch singularity is physical and reflects the absence of collisions (infinite time between scatterings) in the noninteracting theory. In kinetic theory within the relaxation time approximation, infinite scattering time means infinite relaxation time and therefore infinite viscosity 1. To obtain a finite viscosity, scattering processes must be taken into account. These give the plasma particles a non-zero collisional width which shifts the poles of the single particle propagator away from the real axis, thereby regulating the pinch singularity and rendering the limits of zero momentum and energy in Eqs. (2) and (12) well defined and independent of the order in which they are taken. Following Jeon 35 we account for this need for a finite collisional width by organizing the calculation in terms of skeleton diagrams involving full propagators. Extracting the leading order contribution to the viscosity then amounts to specifying for each line in the skeleton diagram individually the required accuracy for the single particle self-energy in powers of the coupling constant.
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21
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hep-ph/0105313
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F. Guerin, hep-ph/0105313;
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Guerin, F.1
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J.M. Martinez Resco (private communication)
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J.M. Martinez Resco (private communication);
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