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.
“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]
The excess of dileptons in the small invariant mass region cannot be explained by charged pion annihilation.
“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]
The data gathered by the SPS from Pb + Pb and Pb + Au collisions, taken together, provide a hint of evidence for a QGP, although many of them could have alternative explanations.
“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]
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.
“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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Gorda, T., Kurkela, A., Paatelainen, R., et al. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.162003 · Cited by 130 · see citing works
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Bluhm, M., Kämpfer, B., Schulze, R., Seipt, D., & Heinz, U. (2007) · Physical Review C · doi:10.1103/physrevc.76.034901 · Cited by 118 · see citing works
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Moreau, P., Soloveva, O., Oliva, L., Song, T., Cassing, W., & Bratkovskaya, E. L. (2019) · Physical Review C · doi:10.1103/physrevc.100.014911 · Cited by 88 · see citing works
“[79] M.”
Alberto Nicolis, A., & Piazza, F. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.011602 · Cited by 87 · see citing works
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Dunne, G. V., Lee, K., & Lu, C. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.3434 · Cited by 87 · see citing works
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Gorda, T., Kurkela, A., Paatelainen, R., et al. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.074015 · Cited by 85 · see citing works
Newman, G. M. (2006) · Journal of High Energy Physics · doi:10.1088/1126-6708/2006/01/158 · Cited by 85 · see citing works
“[11] Michel Le Bellac “Thermal Field Theory” Cambridge University Press, 1996.”
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Alford, M., & Wang, Q. (2005) · Journal of Physics G Nuclear and Particle Physics · doi:10.1088/0954-3899/31/7/017 · Cited by 85 · see citing works
Gagnon, J.-S., & Jeon, S. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.105019 · Cited by 82 · see citing works
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Hong, J., & Teaney, D. A. (2010) · Physical Review C · doi:10.1103/physrevc.82.044908 · Cited by 77 · see citing works
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Dutt-Mazumder, A. K., Alam, J., Roy, P. K., & Sinha, B. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.71.094016 · Cited by 76 · see citing works
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Hidaka, Y., Pu, S., Wang, Q., & Yang, D.-L. (2022) · Progress in Particle and Nuclear Physics · doi:10.1016/j.ppnp.2022.103989 · Cited by 79 · see citing works
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Ayala, A., Sánchez, Á., Piccinelli, G., & Sahu, S. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.71.023004 · Cited by 69 · see citing works
D’Eramo, F., Lekaveckas, M., Liu, H., & Rajagopal, K. (2013) · Journal of High Energy Physics · doi:10.1007/jhep05(2013)031 · Cited by 79 · see citing works
Brown, W. E., Liu, J. T., & Ren, H.-C. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.62.054013 · Cited by 69 · see citing works
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InfluentialKneur, J.-L., Pinto, M. B., Ramos, R. O., et al. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.045020 · Cited by 68 · see citing works
Generalized pions in dense QCD
Rho, M., Wirzba, A., & Zahed, I. (2000) · Physics Letters B · doi:10.1016/s0370-2693(99)01420-3 · Cited by 68 · see citing works
Massless Mode and Positivity Violation in Hot QCD
Su, N., & Tywoniuk, K. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.161601 · Cited by 67 · see citing works
“which can be decomposed into positive and negative helicity-to-chirality contributions, as usual [27].”
BackgroundResultTwo-loop hard thermal loop pressure at finite temperature and chemical potential
Haque, N., Mustafa, M. G., & Strickland, M. T. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.105007 · Cited by 65 · see citing works
Karmakar, B., Ghosh, R., Bandyopadhyay, A., et al. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.094002 · Cited by 65 · see citing works
Constraining warm inflation with CMB data
Mar Bastero-gil, A., Bhattacharya, S., Dutta, K., & Gangopadhyay, M. R. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/02/054 · Cited by 64 · see citing works
Chiral Lagrangian at finite temperature from the Polyakov-chiral quark model
Megías, E., Arriola, E. R., & Salcedo, L. L. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.74.114014 · Cited by 64 · see citing works
Bjoraker, J., & Raju Venugopalan, B. (2001) · Physical Review C · doi:10.1103/physrevc.63.024609 · Cited by 64 · see citing works
“However, the conventional wisdom is that, for transport cross–sections, magnetic screening is also cut off in the infrared by the Debye mass [28, 29].”
BackgroundQuasi-particle description of strongly interacting matter: Towards a foundation
Bluhm, M., Kämpfer, B., Schulze, R., & Seipt, D. (2006) · The European Physical Journal C · doi:10.1140/epjc/s10052-006-0056-y · Cited by 63 · see citing works
Universal Aspects of QCD-like Theories
von Smekal, L. (2012) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/j.nuclphysbps.2012.06.006 · Cited by 68 · see citing works
Calculation of the equation of state of QCD at finite chemical and zero temperature
Zong, H.-S., & Sun, W. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.054001 · Cited by 62 · see citing works
“: zonghs@chenwang.nju.edu.cn. PACS Numbers: 12.38.Aw, 12.38.Lg, 12.39.-x, 24.85.+p 1 The study of the partition function is at the crux of equilibrium statistical field theory (see, for example, Refs. [1,2]). The thermodynamic properties of a system, hence also the equation of state (EOS), are completely determined by…”
BackgroundInfluential
- 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
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