The free energy of hot QED at three and a half loops Page: 1 of 5
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SPhT/94-098 ; ANL-HEP-CP-94-52
THE FREE ENERGY OF HOT QED AT THREE AND A HALF LOOPS
Rajesh R. Parwanit
Service de Physique Theorique, CE-Saclay
F-91191, Gif-sur-Yvette, France
High Energy Physics Division, Argonne National Laboratory
9700 South Cass, II 60439, USA.
The computation of order e4 and e5 contributions to the pressure of massless
quantum electrodynamics at a temperature T is overviewed.
The thermodynamic properties of a QED plasma may be determined from the par-
tition function which can be obtained perturbatively using techniques borrowed from
field theory at zero temperature (T). Indeed, the simplest approach to calculating the
partition function, or the free energy, is to use the imaginary-time formalism whereby
the Feynman rules are as at T = 0 but the energies take on discrete Matsubara values.
However a naive application of these T = 0 like Feynman rules soon leads to
the appearance of power-like infrared (IR) singularities in diagrams. When these IR
singularities from an infinite set of diagrams are resummed, one obtains an expansion
in e2 rather than e2, where e is the QED coupling. The best-known example of
this phenomenon is the e3 plasmon correction to the free energy of QED first found
by Gell-Mann and Brueckner  in the nonrelativistic context and later calculated
relativistically . Physically, the appearance of these IR singularities and the conse-
quent breakdown of the naive perturbative expansion is due to the Debye screening
of electric fields in a plasma. Unlike at T = 0, the particles in the plasma are not
free (modulo ultraviolet renormalisations) but perpetually under the influence of the
In the language of field theory, the Debye screening manifests itself by the non-
vanishing limit IIoo(po = 0, P -> 0) of the electric polarization operator. To lowest
order in the coupling, and in the limit of high temperature, the electric screening
mass-squared is given by a one-loop calculation : m2 =lI(po = 0,f -> 0) = e2T2/3.
Presented at the Workshop of Quantum Infrared Physics, Paris, June 6-10 1994.
t E-mail: email@example.com
01,6TR!BUTION OF THS DOOUM NT iS UN M j2
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Parwani, R. R. & Coriano, C. The free energy of hot QED at three and a half loops, article, February 1, 1995; Illinois. (digital.library.unt.edu/ark:/67531/metadc1273101/m1/1/: accessed December 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.