Gauge field thermodynamics for the SU(2) Yang-Mills system

Engels, Jürgen; Karsch, Frithjof; Satz, Helmut; Montvay, I.

doi:10.1016/0550-3213(82)90077-3

Cited by 267 publications

(184 citation statements)

References 42 publications

Supporting

Mentioning

172

Contrasting

Unclassified

Order By: Relevance

“…(1.1) one can derive all thermodynamic quantities by taking derivatives with respect to a or ~:. For instance the energy density of a gluon gas [8] (including still the vacuum energy density) is given by…”

Section: Z(n~mentioning

confidence: 99%

“…In order to assign absolute values to dimensional quantities like the string tension [1][2][3], glueball mass [3][4][5] or the critical temperature of the gluon gas [6][7][8][9], it is necessary to know the connection between the lattice and continuum scale parameters AL/AMoM [10,11]. This ratio has by now been calculated for different lattice actions [12], including also the contribution of fermions [13] on a four-dimensional euclidean lattice.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of finite-temperature calculations on the lattice, the introduction of different scales in space and time (2 inverse temperature) directions follows quite naturally [7,8]. For simplicity, one uses equal lattice spacings in the three space 285 directions ai --a and an independent spacing in the time direction, a4 = aT.…”

Section: Introductionmentioning

confidence: 99%

“…During the past year much progress has been made in extracting physically interesting quantities out of Monte Carlo simulations of non-abelian gauge theories on the lattice [1][2][3][4][5][6][7][8][9]. In order to assign absolute values to dimensional quantities like the string tension [1][2][3], glueball mass [3][4][5] or the critical temperature of the gluon gas [6][7][8][9], it is necessary to know the connection between the lattice and continuum scale parameters AL/AMoM [10,11].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

SU(N) gauge theory couplings on asymmetric lattices

1982

View full text Add to dashboard Cite

The connection between euclidean and hamiltonian lattice QCD requires the use of asymmetric lattices, which in turn implies the necessity of two coupling parameters. We analyse the dependence of space-and time-like couplings g,, and g~ on the different lattice spacings a and aT in space and time directions. Using the background field method we determine the derivatives of the couplings with respect to the asymmetry factor ~ = a/a~ in the weak coupling limit, obtaining We argue that the sum of these derivatives has to be equal to b0 = 11N/487r 2 and determine the A parameter for asymmetric lattices. In the limit ~ ~ co all our results agree with those of A. and P. Hasenfratz.

show abstract

Section: Z(n~mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

SU(N) gauge theory couplings on asymmetric lattices

1982

View full text Add to dashboard Cite

show abstract

“…On the other hand, the variation of e G in fig. 1 appears still more rapid than the second order transition of the SU(2) Yang-Mills system [15]: in both cases, e/ T 4 requires about 20AL to rise from "bottom to top"; but ASU(2)/ASL U(3) ~ 2_We note further that at high T our eG(T ) approaches the Stefan-Boltzmann limit; but it does so much slower than for the pure YangMills systems, and from above.…”

Section: P~rpomentioning

confidence: 99%

Deconfinement and virtual quark loops

1983

Self Cite

View full text Add to dashboard Cite

We calculate per Monte Carlo evaluation on an 83 × 3 lattice the energy density e G of the gluon sector of QCD, including virtual quark loops up to the fourth power in the hopping parameter expansion. For light quarks of one flavour, we observe at T/A L ~ 95 -+ 10 a rapid variation of e G in T, accompanied by strong fluctuations from iteration to iteration, as clear signal of the deconfinement transition.The deconfinement transition, at which strongly interacting matter becomes a colour-conducting plasma, has so far been studied for pure Yang-Mills systems and for full QCD without virtual quark loops ("quenched approximation"). The concentration on Yang-Mills fields in the first studies of the phenomenon is physically meaningful: non-abelian gauge fields alone already exhibit confinement at low [1,2] and deconfinement at high [3] temperatures, at least on the lattice. The statistical mechanics of SU(N) gauge fields ,1 has therefore contributed significantly to our understanding of colour force thermodynamics. On the other hand, the neglect of virtual quark loops in the extension of full QCD is due to technical difficulties rather than to physical reasoning: the evaluation of the r X r fermion matrix, where r is some multiple of the number of lattice sites (typically 10 000 or more), quickly led to the limits of computer possibilities both in speed and in memory space. Nevertheless, it is the virtual quark loops which provide the "breaking of the string" through meson formation, so their role in deconfinement is certainly crucial. The advent of array processors has now put the inclusion of fermions within reach, and the aim of this paper is to present first results on the statistical mechanics of 1 Alexander yon Humboldt fellow, on leave from Hacettepe University, Ankara, Turkey. ,1 Fora survey see ref. A phase transition can be studied in two ways. We may consider some thermodynamic quantity -energy density, specific heat -and look for a discontinuity or singularity; or we may construct a specific order parameter to distinguish the two phases. Thus, in the Ising model, the Curie point can be characterized either by the singularity of the specific heat or through the vanishing of the spontaneous magnetization.In SU(N) Yang-Mills theory, deconfinement is related to the breaking of a global Z N symmetry [6,7]. The euclidean formulation of the partition function

show abstract

QCD at finite temperature

Kalashnikov

1984

Fortschr. Phys.

119

View full text Add to dashboard Cite

Quantum chromodynamics is studied a t finite temperatures and densities using the temperature Green functions method. For the Green functions the renormalized Schwinger-Dyson equations are obtained and their qualitative properties are discussed. The equality of the renormalization constants for the equations obtained a t T, p =+ 0 with those for quantum field theory is pointed out. General properties of the gluon polarization tensor are investigated a t T, ,u + 0. The temperature Green functions are calculated within the one-loop approximation using both relativistic and axial gauges. The fulfilment of the Slavnov-Taylor identities is verified. The asymptotic behaviour of the polarization tensor a t T, ,u =+= 0 is established and the excitation spectrum of quarkgluon plasma is found. Both Fermi and Bose excitations are considered and the gauge invariance of the spectra is demonstrated. The renormalization group extension of the dispersion laws into the regions of high temperatures and densities is presented. The exact representation of the thermodynamical potential in QCD is found in terms of the temperature Green functions. For the quarkgluon plasma the thermodynamical potential is calculated with the g3-term taken into account. The equat.ion of state of the hot quark-gluon plasma is found and its properties are discussed. The complete evolutional diagram of the hadronic matter is outlined. The phase curve asymptotics, which put bounds on the quark-gluon plasma domain, are found for the two limiting cases ( p = 0, T + To; T = 0, ,u + po). The phase transition of the hot quark-gluon plasma placed in external Abelian field is studied. The instability of such plasma has been found and the program of its stabilization is indicated. The infrared behaviour of the non-Abelian gauge theory is studied for finite temperatures when power divergencies are essential. The propagator of transverse gluons is shown to be singular for momenta IpI -g2T and this cannot be avoided by summing the simplest bubble chains. The infrared asymptotic behaviour of the tree-gluon vertex is found and the results obtained are checked using the Slavnov-Taylor identities. The Green functions asymptotics found indicate either an instability of the quark-gluon plasma in the infrared momentum domain or the inconsistency of the perturbational methods. A non-perturbative approach to the infrared problem in QCD is developed within the axial gauge. The closed equations for the structure functions that determine the gluon polarization tensor are obtained by using the Slavnov-Taylor identities-to found approximately the three-gluon vertex. It is shown that the solution of the equationg. obtained by iterations does not remove the infrared singularity from the temperature Green fuiictions. The nonperturbative solution of such equations is discussed.

show abstract

Gauge field thermodynamics for the SU(2) Yang-Mills system

Cited by 267 publications

References 42 publications

SU(N) gauge theory couplings on asymmetric lattices

SU(N) gauge theory couplings on asymmetric lattices

Deconfinement and virtual quark loops

QCD at finite temperature

Contact Info

Product

Resources

About