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Hydrodynamic transport functions from quantum kinetic theory
High Energy Physics - Phenomenology · Submitted 13 Oct 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Hu, Phys. Rev. D37, 2878 (1988)] constructed from the closed-time-path (CTP), two-particle-irreducible (2PI) effective action we show how to compute from first principles the shear and bulk viscosity functions in the hydrodynamic-thermodynamic regime.
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Starting from the quantum kinetic field theory [E. Calzetta and B. L. Hu, Phys. Rev. D37, 2878 (1988)] constructed from the closed-time-path (CTP), two-particle-irreducible (2PI) effective action we show how to compute from first principles the shear and bulk viscosity functions in the hydrodynamic-thermodynamic regime. For a real scalar field with $\lambda \Phi ^{4}$ self-interaction we need to include 4 loop graphs in the equation of motion. This work provides a microscopic field-theoretical basis to the ``effective kinetic theory'' proposed by Jeon and Yaffe [S. Jeon and L. G. Yaffe, Phys. Rev. D53, 5799 (1996)], while our result for the bulk viscosity reproduces their expression derived from linear response theory and the imaginary-time formalism of thermal field theory. Though unavoidably involved in calculations of this sort, we feel that the approach using fundamental quantum kinetic field theory is conceptually clearer and methodically simpler than the effective kinetic theory approach, as the success of the latter requires clever rendition of diagrammatic resummations which is neither straightforward nor failsafe. Moreover, the method based on the CTP-2PI effective action illustrated here for a scalar field can be formulated entirely in terms of functional integral quantization, which makes it an appealing method for a first-principles calculation of transport functions of a thermal non-abelian gauge theory, e.g., QCD quark-gluon plasma produced from heavy ion collisions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Starting from the quantum kinetic field theory [E. Calzetta and B. L. | method 0.72 | 0.33 | 0.03 | unclear 0.89 |
| s1 | Hu, Phys. Rev. D37, 2878 (1988)] constructed from the closed-time-path (CTP), two-particle-irreducible (2PI) effective action we show how to compute from first principles the shear and bulk viscosity functions in the hydrodynamic-thermodynamic regime. | contribution 0.89 | 0.90 | 0.66 | asserted 1.00 |
| s2 | For a real scalar field with $\lambda \Phi ^{4}$ self-interaction we need to include 4 loop graphs in the equation of motion. | method 0.99 | 0.70 | 0.04 | asserted 1.00 |
| s3 | This work provides a microscopic field-theoretical basis to the ``effective kinetic theory'' proposed by Jeon and Yaffe [S. Jeon and L. G. | contribution 0.62 | 0.67 | 0.20 | asserted 1.00 |
| s4 | Yaffe, Phys. Rev. D53, 5799 (1996)], while our result for the bulk viscosity reproduces their expression derived from linear response theory and the imaginary-time formalism of thermal field theory. | result 0.92 | 0.82 | 0.22 | asserted 1.00 |
| s5 | Though unavoidably involved in calculations of this sort, we feel that the approach using fundamental quantum kinetic field theory is conceptually clearer and methodically simpler than the effective kinetic theory approach, as the success of the latter requires clever rendition of diagrammatic resummations which is neither straightforward nor failsafe. | interpretation 0.92 | 0.32 | 0.20 | asserted 0.85 |
| s6 | Moreover, the method based on the CTP-2PI effective action illustrated here for a scalar field can be formulated entirely in terms of functional integral quantization, which makes it an appealing method for a first-principles calculation of transport functions of a thermal non-abelian gauge theory, e.g., QCD quark-gluon plasma produced from heavy ion collisions. | future work 0.49 | 0.43 | 0.15 | asserted 0.51 |
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Original abstract
Starting from the quantum kinetic field theory [E. Calzetta and B. L. Hu, Phys. Rev. D37, 2878 (1988)] constructed from the closed-time-path (CTP), two-particle-irreducible (2PI) effective action we show how to compute from first principles the shear and bulk viscosity functions in the hydrodynamic-thermodynamic regime. For a real scalar field with $\lambda \Phi ^{4}$ self-interaction we need to include 4 loop graphs in the equation of motion. This work provides a microscopic field-theoretical basis to the ``effective kinetic theory'' proposed by Jeon and Yaffe [S. Jeon and L. G. Yaffe, Phys. Rev. D53, 5799 (1996)], while our result for the bulk viscosity reproduces their expression derived from linear response theory and the imaginary-time formalism of thermal field theory. Though unavoidably involved in calculations of this sort, we feel that the approach using fundamental quantum kinetic field theory is conceptually clearer and methodically simpler than the effective kinetic theory approach, as the success of the latter requires clever rendition of diagrammatic resummations which is neither straightforward nor failsafe. Moreover, the method based on the CTP-2PI effective action illustrated here for a scalar field can be formulated entirely in terms of functional integral quantization, which makes it an appealing method for a first-principles calculation of transport functions of a thermal non-abelian gauge theory, e.g., QCD quark-gluon plasma produced from heavy ion collisions.
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3 arXiv papers cite this in 3 sentences
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This calculation has been in done in scalar theory [ref] and has been reproduced since then using different methods (e.g. real-time formalism [ref] , direct ladder summation in Euclidean space [ref] , 2PI effective action methods [ref] and quantum kinetic field theory derived from the closed-time-path 2PI effective action [ref] ).
Leading Order Calculation of Shear Viscosity in Hot Quantum Electrodynamics from Diagrammatic Methods · Introduction · 0.86
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For other approaches see [ref] , [ref] , [ref] and [ref] with references therein.
Towards precise calculation of transport coefficients in the hadron gas. The shear and the bulk viscosities · Conditions of applicability · 0.97
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