Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-03-25
Int.J.Mod.Phys. A14 (1999) 2921-2948
Physics
High Energy Physics
High Energy Physics - Theory
37 pages, 12 figures, typos corrected, references added, Introduction rewritten
Scientific paper
10.1142/S0217751X99001421
We consider various ways of treating the infrared divergence which appears in the dynamically generated fermion mass, when the transverse part of the photon propagator in N flavour $QED_{3}$ at finite temperature is included in the Matsubara formalism. This divergence is likely to be an artefact of taking into account only the leading order term in the $1 \over N$ expansion when we calculate the photon propagator and is handled here phenomenologically by means of an infrared cutoff. Inserting both the longitudinal and the transverse part of the photon propagator in the Schwinger-Dyson equation we find the dependence of the dynamically generated fermion mass on the temperature and the cutoff parameters. It turns out that consistency with certain statistical physics arguments imposes conditions on the cutoff parameters. For parameters in the allowed range of values we find that the ratio $r=2*Mass(T=0)/critical temperature$ is approximately 6, consistently with previous calculations which neglected the transverse photon contribution.
Lee Dominic
Metikas Georgios
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