A continuum order parameter for deconfinement Page: 1 of 7
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A CONTINUUM ORDER PARAMETER
C. D. ROBERTS
Physics Division 203, Argonne National Laboratory
'N"I STERArgonne, IL 60439-4843, USA
Dyson-Schwinger equations are presented as a nonperturbative tool for
the study and modelling of QCD at finite-T. An order parameter for de-
confinement, applicable for both light and heavy quarks, is introduced.
In a simple Dyson-Schwinger equation model of two-flavour QCD, coin-
cident, 2nd-order chiral symmetry restoration and deconfinement transi-
tions occur at T ~ 150 MeV, with the same critical exponent, 6 ~ 0.33.
1. Introduction. The Dyson-Schwinger equations [DSEs] provide a non-
perturbative, continuum approach to solving a quantum field theory; familiar
examples are: the gap equation in superconductivity; the Bethe-Salpeter equa-
tion, which describes relativistic 2-body bound states, such as mesons com-
posed of light quarks; and the covariant Fadde'ev equation, which describes
relativistic 3-body bound states, such as baryons. The DSEs are a system of
coupled integral equations, whose solutions are the Schwinger functions (Eu-
clidean propagators), and a weak coupling expansion of the DSEs reproduces
all of the diagrams of perturbation theory. Therefore, in any modelling of QCD
in this approach, one has a tight constraint on the behaviour of the solution
of the DSEs at large spacelike-q2. The DSEs thereby provide a means of
extrapolating what is known about the QCD Schwinger functions at large-q2
into the small-q2 (infrared) regime.
The nonperturbative nature of the DSEs entails that they provide a natural
framework for the study of confinement, dynamical chiral symmetry breaking
[DCSB] and observable effects of bound state substructure. In recent years
there have been many successful applications of the framework to the calcula-
tion of exclusive processes at zero temperature. The approach is distinguished
by the feature that it unifies the treatment of both hard and soft physics; i.e.,
once a model for the infrared behaviour of the connected gluon 2-point func-
tion (gluon propagator) is chosen, one can calculate observables on the entire
range of accessible energies and momentum transfers, as illustrated in Refs. .
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Roberts, C.D. A continuum order parameter for deconfinement, article, March 1, 1997; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc681899/m1/1/: accessed May 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.