The Ohio State University
The series appears to converge only for such extremely small values
that T is approaching the grand unification scale.
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should give a sequence of approximations
with successively smaller errors
should reduce to the weak-coupling expansion in the limit
should match on to lattice gauge theory results (equation of state, etc.)
for intermediate values of
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exact gauge invariance:
approximate thermodynamic consistency: higher order in
running of via renormalization group
tractable at order (calculation in progress)
can be generalized to order , but magnetic mass problem at order
approximate gauge invariance:
higher order in
exact thermodynamic consistency:
incorrect running of
intractable (requires solving integral equation for gluon propagator)
(Blaizot, Iancu, and Rebhan)
gauge invariant by neglecting gauge-dependent terms
approximate thermodynamic consistency
running of via simple substitution
no obvious generalization to higher order in