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Thermal Field Theory
Abstract
Now in paperback, this text introduces the theoretical framework for describing the quark-gluon plasma, an important new state of matter. The first part of this book is a self-contained introduction to relativistic thermal field theory. Topics include the path integral approach, the real and the imaginary time formalisms, fermion fields and gauge fields at finite temperature. Useful techniques such as the evaluation of frequency sums or the use of cutting rules are illustrated on various examples. The second part of the book is devoted to recent developments, giving a detailed account of collective excitations (bosonic and fermionic), and showing how they give rise to energy scales which imply a reorganization of perturbation theory. The relation with kinetic theory is also explained. Applications to processes which occur in heavy ion collisions and in astrophysics are worked out in detail. Each chapter ends with exercises and a guide to the literature.
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“A summary of the results of these efforts mainly through the Pb + Pb experiments at SPS-CERN provided compelling evidence in favor of the existence of a new state of matter[23].”
From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [23]
In the citing paper
“The excess of dileptons in the small invariant mass region cannot be explained by charged pion annihilation [23].”
From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [23]
In the citing paper
“We summarize the observables that have been proposed as telltales of a QGP and the data gathered by the SPS from Pb + Pb and Pb + Au collisions, which taken together provide a hint of evidence [22, 23, 120, 129] for a QGP, although many of them could have alternative explanations.”
From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [23]
In the citing paper
“The current understanding of these features is that the medium effects result in a shift in the ρ meson mass as well as a change in its width[23, 120, 135].”
From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [23]
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Items 501–600 of 899
Operator product expansion for the thermal correlator of scalar currents
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“Throughout this work, we employ the real-time formulation of the thermal field theory [10, 11].”
MethodShear viscosity of the Φ4 theory from classical simulation
Homor, M. M., & Jakovác, A. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.92.105011 · Cited by 8
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Thermal renormalization group equations and the phase transition of scalar O(N) theories
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“These are given in [18, 33]: ρ± (ω, k) = z±(k)δ (ω − ω±(k)) + z∓(k)δ (ω + ω± (k)) + β± (ω, k)Θ ( k(2) − ω(2) )”
Collective modes of ultra-relativistic magnetoactive electron plasma
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Das, A., & Kalauni, P. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.93.125028 · Cited by 8
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“This is why it is expected that chiral symmetry is restored at enough high T .”
BackgroundScalar correlations in a quark plasma and low mass dilepton production
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Petrov, K. (2005) · The European Physical Journal C · doi:10.1140/epjc/s2005-02329-3 · Cited by 8
“e −Ĥ/T 〉T denotes the thermal average [26].”
MethodAnomalous pseudoscalar-photon vertex in and out of equilibrium
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Dynamics of heavy quarks in strongly coupled $$ \mathcal{N} $$ = 4 SYM plasma
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Heavy-quark potential in the Gribov-Zwanziger approach around the deconfinement phase transition
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Thermal effects in freeze-in neutrino dark mater production
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Quark production and thermalization of the quark-gluon plasma
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Quark saturation in the QCD phase diagram
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Marquez, F. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.89.076010 · Cited by 7
Validating the 2PI resummation: The Bloch-Nordsieck example
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Cartas-Fuentevilla, R., Berra–Montiel, J., & Meza-Aldama, O. (2020) · The European Physical Journal C · doi:10.1140/epjc/s10052-020-8161-x · Cited by 7
Non-perturbative effects for dark sectors with QCD portals
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Infrared behavior of the dispersion relations in high-temperature scalar QED
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Electromagnetic effects of neutrinos in an electron gas
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Chiral transition and mesonic excitations for quarks with thermal masses
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Hamada, M., Kouno, H., Nakamura, A., et al. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.81.094506 · Cited by 7
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Farooq, H., Sarfraz, M., Iqbal, Z., et al. (2017) · Chinese Physics B · doi:10.1088/1674-1056/26/11/110301 · Cited by 7
Trans-Planckian effects in warm inflation
Nezhad, H. B., & Shojai, F. (2019) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2019/07/002 · Cited by 7
“ty A=L3, and therefore V R = A=L3. The calculation of the Helmholtz free energy of a radiation eld has been done in the framework of nite temperature quantum eld theory and the result for V R(˚;T) is [32,33] V R(˚;T) = 1 90 ˇ2g ?T 4 + 1 2 (m T)2˚2 + ::: (3) where g ?(T) is the eective degrees of freedom of radiation e…”
MethodAbreu, L. M., & Nery, E. S. (2019) · The European Physical Journal A · doi:10.1140/epja/i2019-12793-3 · Cited by 7
Infrared finiteness of a complete theory of charged scalars and fermions at finite temperature
Sen, P., Indumathi, D., & Choudhury, D. (2020) · The European Physical Journal C · doi:10.1140/epjc/s10052-020-08498-3 · Cited by 7
Viscosity over entropy ratio in a quark plasma
Czerski, P., Alberico, W. M., Chiacchiera, S., Pace, A. D., Hansen, H., Molinari, A., & Nardi, M. (2008) · Journal of Physics G Nuclear and Particle Physics · doi:10.1088/0954-3899/36/2/025008 · Cited by 7
Phenomenological Tsallis distribution from thermal field theory
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Quantum color screening in external magnetic field
Huang, G., Zhao, J., & Zhuang, P. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.114035 · Cited by 7
Chemical nonequilibrium for interacting bosons: Applications to the pion gas
Fernández-Fraile, D., & Nicola, Á. G. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.056003 · Cited by 7
LeClair, A. (2007) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/40/31/033 · Cited by 7
Brandt, F. T., Das, A., Frenkel, J., et al. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.64.065018 · Cited by 7
Hard thermal effective actions in the Schwinger formulation
Das, A., & Frenkel, J. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.75.025021 · Cited by 7
Reaction-rate formula in out-of-equilibrium quantum-field theory
Niégawa, A., Okano, K., & Ozaki, H. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.056004 · Cited by 7
Complex gap in color superconductivity
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Nonequilibrium effects and baryogenesis
Charng, Y.-Y., Lee, D.-S., Leung, C. N., et al. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.72.123517 · Cited by 7
Das, A., & Haque, N. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.054008 · Cited by 6
Castaño‐Yepes, J. D., & Muñoz, E. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.076028 · Cited by 6
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Neutrino spectral density at electroweak scale temperature
Miura, K., Hidaka, Y., Satow, D., & Kunihiro, T. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.88.065024 · Cited by 6
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Andersen, J. O. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.57.5004 · Cited by 6
“Bx”
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On the (in)consistency of perturbation theory at finite temperature
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Karkout, O., Papaefstathiou, A., Postma, M., Tetlalmatzi-Xolocotzi, G., van de Vis, J., & Pree, T. D. (2024) · Journal of High Energy Physics · doi:10.1007/jhep11(2024)077 · Cited by 6
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Fate of non-Fermi-liquid behavior in QED3 at finite chemical potential
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ULTRASOFT QUARK DAMPING IN HOT QCD
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Electromagnetic mass difference of pions at low temperature
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THERMOFIELD DYNAMICS AND e+e- REACTIONS
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“The sum is then evaluated using the usual contour technique [69, 70].”
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“(B6) This representation allows us to carry out the sum over the Matsubara frequencies ωm in a rather straightforward manner [18, 19]: 1 β ∑”
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Quark propagation in the quark-gluon plasma
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Gauge dependence of the fermion quasiparticle poles in hot gauge theories
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LeClair, A. (2006) · CERN Document Server (European Organization for Nuclear Research) · Cited by 6
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Smart holes: analogue black holes with the right temperature and entropy
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Quantum properties of a non-Gaussian state in the large- N approximation
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Quantum electromagnetic phenomena far from small evaporating black holes
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“It is a consequence of the requirements needed to formulate a physically acceptable quantum field theory (e.g., Haag 1996) that quantum operators localised in a certain space-time region probe the vacuum as if it is a non-empty state.”
BackgroundMethodGeneralized Stueckelberg-Higgs Gauge Theory
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“It is also known that in plasma physics there is a shielding phenomenon where the interaction mediated by the gauge field becomes short-ranged with the gauge field acquiring a mass - the socalled Debye mass [21] and there is also the possibility of exploring the concept of restoration of symmetry (Jackiw-Dolan) above…”
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Higher-form symmetry and chiral transport in real-time Abelian lattice gauge theory
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Photon self-energy at all temperatures and densities in all of phase space
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Weak magnetic field effects on chiral critical temperature in a nonlocal Nambu–Jona-Lasinio model
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Electric screening mass of the gluon with gluon condensate at finite temperature
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“The magnitude of me influences strongly the existence or non-existence of charmonium in the high temperature phase according the following behaviour of the potential V (r) between gauge invariant sources [22]:”
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Emergence of soft quark excitations by the coupling with a soft mode of the QCD critical point
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“The spectral properties of fermions at nonzero μ have been studied in gauge theories in the hard dense limit [31] and also the electron spectrum in high density plasma [44].”
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Dynamics of hot gauge theories
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Are there Goldstone bosons in d≤z+1 ?
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Metadata
- Authors
- Le Bellac, M.
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 1996-08-01
- OpenAlex
- W4210557146
- Cited by
- 897
- References
- 0
- Citations by year
- 2026: 20 · 2025: 35 · 2024: 28 · 2023: 30 · 2022: 25 · 2021: 32 · 2020: 54 · 2019: 28 · 2018: 21 · 2017: 25 · 2016: 22 · 2015: 32 · 2014: 36 · 2013: 40 · 2012: 38
- FWCI
- 13.98
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › High-Energy Particle Collisions Research
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Keywords
- thermal field theory, quark-gluon plasma, path integral, imaginary time formalism, real-time formalism, fermion fields, gauge fields, cutting rules, collective excitations, kinetic theory, heavy-ion collisions, astrophysical plasmas
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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