Application of the heat-kernel method to the constituent quark model at finite temperature

Schaefer, Bernd-Jochen; Pirner, H. J.

doi:10.1016/s0375-9474(97)00601-5

Cited by 20 publications

(25 citation statements)

References 16 publications

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“…The parameters of the linear σ-model are fixed at zero temperature as in ref. [7]. Because the theory is strongly coupled we cannot calculate the low-energy theory directly.…”

Section: Renormalization Group Flow Equationsmentioning

confidence: 99%

“…For details we refer the reader to ref. [7]. A prime on the potential denotes differentiation with respect to the fields φ 2 and we elucidate our notation by the equation…”

Section: Renormalization Group Flow Equationsmentioning

confidence: 99%

“…[7,9]). Consider for example the RG improved leading-order contribution to the one-loop potential of a scalar one-component theory in a sharp cutoff regularization, within the momentum shell k ≤ p ≤ Λ, (for simplicity we show it for the second term of Eq.…”

Section: Renormalization Group Flow Equationsmentioning

confidence: 99%

“…ref. [7]) the flow equation contributions have the typical form 1/(k 2 + mass 2 ) and are sometimes called "threshold functions" [15]. This structure controls the decoupling of the massive modes in the infrared.…”

Section: Renormalization Group Flow Equationsmentioning

confidence: 99%

“…As shown in the appendix of ref. [7] it is possible to split the thermal fluctuations into a zero temperature contribution plus a finite temperature contribution using the so-called generalized Θ-function transformation. However, in the present work we decided to solve the Matsubara sums numerically and do not apply the Θ-function transformation.…”

Section: Finite-temperature Flow Equationmentioning

confidence: 99%

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Convergence of the expansion of the renormalization group flow equation

et al. 2000

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We compare and discuss the dependence of a polynomial truncation of the effective potential used to solve exact renormalization group flow equation for a model with fermionic interaction (linear sigma model) with a grid solution. The sensitivity of the results on the underlying cutoff function is discussed. We explore the validity of the expansion method for second and first-order phase transitions.

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“…The parameters of the linear σ-model are fixed at zero temperature as in ref. [7]. Because the theory is strongly coupled we cannot calculate the low-energy theory directly.…”

Section: Renormalization Group Flow Equationsmentioning

confidence: 99%

“…For details we refer the reader to ref. [7]. A prime on the potential denotes differentiation with respect to the fields φ 2 and we elucidate our notation by the equation…”

Section: Renormalization Group Flow Equationsmentioning

confidence: 99%

Section: Renormalization Group Flow Equationsmentioning

confidence: 99%

Section: Renormalization Group Flow Equationsmentioning

confidence: 99%

Section: Finite-temperature Flow Equationmentioning

confidence: 99%

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Convergence of the expansion of the renormalization group flow equation

et al. 2000

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Chiral symmetry breaking in hot matter

Klevansky

Hadrons in Dense Matter and Hadrosynthesis

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This series of three lectures covers (a) a basic introduction to symmetry breaking in general and chiral symmetry breaking in QCD, (b) an overview of the present status of lattice data and the knowlegde that we have at finite temperature from chiral perturbation theory. (c) Results obtained from the Nambu--Jona-Lasinio model describing static mesonic properties are discussed as well as the bulk thermodynamic quantities. Divergences that are observed in the elastic quark-antiquark scattering cross-section, reminiscent of the phenomenon of critical opalescence in light scattering, is also discussed. (d) Finally, we deal with the realm of systems out of equilibrium, and examine the effects of a medium dependent condensate in a system of interacting quarks.Comment: 62 LaTex pages, incorporating 23 figures. Lectures given at the eleventh Chris-Engelbrecht Summer School in Theoretical Physics, 4-13 February, 1998, to be published by Springer Verla

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Pressure and interaction measure of the gluon plasma

2010

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We explore the thermodynamics of the gluon plasma in SU(3) Yang-Mills theory emerging from the non-trivial spatial dynamics of valence gluons. The lattice data suggest that these gluons interact with each other linearly at large spatial separations. At high temperatures, valence gluons should reproduce the pressure of the non-interacting Stefan-Boltzmann plasma along with the leading perturbative correction. These properties of valence gluons can be modeled in terms of the integral over their trajectories. We calculate such a world-line integral analytically and obtain the pressure and the interaction measure $(\varepsilon-3p)/T^4$ of the gluon plasma. Additionally, we account for the contributions of stochastic background fields to these thermodynamic quantities. The results turn out to be in a good agreement with the corresponding lattice data. In particular, the lattice-simulated peak of the interaction measure near the deconfinement critical temperature is reproduced.Comment: 20 pages, 5 figures. Final version. To appear in Nucl. Phys.

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Application of the heat-kernel method to the constituent quark model at finite temperature

Abstract: The Heat Kernel Method is applied to the constituent quark model.

Cited by 20 publications

References 16 publications

Convergence of the expansion of the renormalization group flow equation

Convergence of the expansion of the renormalization group flow equation

Chiral symmetry breaking in hot matter

Pressure and interaction measure of the gluon plasma

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