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Spectral representation of the shear viscosity for local scalar QFTs at finite temperature
High Energy Physics - Theory · Submitted 27 Apr 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, $\eta_{0}$.
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The abstract, sentence by sentence
In local scalar quantum field theories (QFTs) at finite temperature correlation functions are known to satisfy certain non-perturbative constraints, which for two-point functions in particular implies the existence of a generalisation of the standard K\"{a}ll\'{e}n-Lehmann representation. In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, $\eta_{0}$. As an example, we calculate $\eta_{0}$ in $\phi^{4}$ theory, establishing its leading behaviour in the small and large coupling regimes.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In local scalar quantum field theories (QFTs) at finite temperature correlation functions are known to satisfy certain non-perturbative constraints, which for two-point functions in particular implies the existence of a generalisation of the standard K\"{a}ll\'{e}n-Lehmann representation. | background 1.00 | 0.04 | 0.05 | asserted 1.00 |
| s1 | In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, $\eta_{0}$. | contribution 0.85 | 0.96 | 0.51 | asserted 1.00 |
| s2 | As an example, we calculate $\eta_{0}$ in $\phi^{4}$ theory, establishing its leading behaviour in the small and large coupling regimes. | result 0.72 | 0.96 | 0.21 | asserted 1.00 |
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The paper
Original abstract
In local scalar quantum field theories (QFTs) at finite temperature correlation functions are known to satisfy certain non-perturbative constraints, which for two-point functions in particular implies the existence of a generalisation of the standard K\"{a}ll\'{e}n-Lehmann representation. In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, $\eta_{0}$. As an example, we calculate $\eta_{0}$ in $\phi^{4}$ theory, establishing its leading behaviour in the small and large coupling regimes.
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How the literature uses it
8 arXiv papers cite this in 11 sentences
Papers citing it · 9 sentences without a confident label
Cites it as background 2 papers
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We will not discuss further here the specific structure of thermoparticle contributions and their corresponding damping factors, only to mention that their properties have been explored in different models [ref] , and that more recently in Refs. [ref] and [ref] it was shown that these quantities can in fact be used to perform non-perturbative analytic calculations of different in-medium observables, including the shear viscosity.
Pseudo-scalar meson spectral properties in the chiral crossover region of QCD · Thermoparticles · 0.83
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Alternatively, several non-perturbative quantum field theory techniques have been developed to calculate $η/s$ as well [ref] .
Shear viscosity from perturbative Quantum Chromodynamics to the hadron resonance gas at finite baryon, strangeness, and electric charge densities · Introduction · 0.96
What it cites · 49 sentences without a confident label
Uses the method or tool of 1 paper
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In particular, by applying the procedure outlined in Sec. [ref], and demanding that the equation of motion[In Ref. [ref] the $1/3!$ factor was not included in Eq. [ref], but here and throughout this paper we will use this in order to be consistent with the perturbative convention.] operator [equation] is suppressed in all correlation functions of the asymptotic field $ϕ_0$, in Ref. [ref] the authors were able to explicitly calculate the form of the damping factor $D_m,β(u⃗)$ for both $λ<0$ and $λ>0$.
Asymptotic dynamics of thermal quantum fields · Thermal particle shear viscosity in $ϕ^4$ theory · 0.82
Compares with 3 papers
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Whilst it might appear surprising that $η_0$ is divergent, since perturbative calculations have been performed in this model [ref] , it should be noted that the divergence of $η_0$ is a non-perturbative result, and so does not necessarily need to coincide with perturbative expectations.
Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory · Positive coupling shear viscosity · 0.90
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Whilst it might appear surprising that $η_0$ is divergent, since perturbative calculations have been performed in this model [ref] , it should be noted that the divergence of $η_0$ is a non-perturbative result, and so does not necessarily need to coincide with perturbative expectations.
From Quantum Field Theory to Hydrodynamics: Transport Coefficients and Effective Kinetic Theory · Positive coupling shear viscosity · 0.90
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Equation [ref] coincides in structure with the lowest order perturbative calculation of $ρ_ππ$ [ref] , although the representation in Eq. [ref] is non-perturbative.
Computing Spectral Densities in Finite Temperature Field Theory · Analytic structure of the shear viscosity · 0.97
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