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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 301–400 of 899
Kinetic description of charmonium production in high-energy nuclear collisions
Alberto Polleri, A., Thorsten Renk, A., Schneider, R., & Weise, W. (2004) · Physical Review C · doi:10.1103/physrevc.70.044906 · Cited by 22
Equilibration of the chiral asymmetry due to finite electron mass in electron-positron plasma
Boyarsky, A. M., Cheianov, V., Oleg Ruchayskiy, C., & Sobol, O. O. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.013003 · Cited by 22
“[59] M.”
BackgroundInfluentialNew method for directly computing reduced density matrices
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Scalar gravitational waves in the effective theory of gravity
Mottola, E. (2017) · Journal of High Energy Physics · doi:10.1007/jhep07(2017)043 · Cited by 46
“As is well known in finite temperature field theory, plasmas or generally whenever there is a polarizable fluctuating medium, the fluctuations of the charges in the medium induce through Gauss’ law a collective plasmon mode described by a propagating longitudinal electric field [59].”
BackgroundMomentum and its affiliated transport coefficients for hot QCD matter in a strong magnetic field
Rath, S., & Patra, B. K. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.036011 · Cited by 21
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Effective CP violation in the Standard Model
Smit, J. (2004) · UvA-DARE (University of Amsterdam) · Cited by 21
Out of Equilibrium Quantum Field Theory
Niégawa, A. (1999) · Progress of Theoretical Physics · doi:10.1143/ptp.102.1 · Cited by 21
Momentum broadening of a fast parton in a perturbative quark-gluon plasma
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“However, such a plasma is unstable due to the chromomagnetic modes (for a review see [8]).”
BackgroundStandard model as the topological material
Воловик, Г. Е., & Zubkov, M. A. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aa573d · Cited by 22
Thermoelectric properties of the (an-)isotropic QGP in magnetic fields
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Geometrically confined thermal field theory: Finite size corrections and phase transitions
Mogliacci, S., Kolbé, I., & Horowitz, W. A. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.116017 · Cited by 20
Scalar gravitational waves in the effective theory of gravity
Mottola, E. (2021) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · doi:10.1007/jhep07%282017%29043 · Cited by 27
Out-of-equilibrium electromagnetic radiation
Serreau, J. (2004) · Journal of High Energy Physics · doi:10.1088/1126-6708/2004/05/078 · Cited by 21
Leptonic contribution to the bulk viscosity of nuclear matter
Alford, M., & Good, G. J. (2010) · Physical Review C · doi:10.1103/physrevc.82.055805 · Cited by 20
Wu, C., & Lee, D.-S. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.71.125005 · Cited by 21
Dadić, I. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.59.125012 · Cited by 20
“Contrary to the equilibrium case([1, 2]) where pinch, collinear, and infrared problems have been successfully controlled([3, 4, 5, 6]), out of equilibrium theory([7, 8, 9]) has suffered from them to these days.”
BackgroundGluon Scattering in = 4 Super Yang-Mills at Finite Temperature
Ito, K., Năstase, H., & Iwasaki, K. (2008) · Progress of Theoretical Physics · doi:10.1143/ptp.120.99 · Cited by 20
“…+ n4) (2π)4δ(4)(p1 + p2 − p3 − p4) ¯|M|2[Φ1 + Φ2 − Φ3 − Φ4]2 (4.7) where νg = 16 is the sum over colours and spins on the out state, ¯|M|2 is the gluon scattering amplitude squared summed over spins and colours in final state and averaged over the same in the initial state (thus is related to…”
InfluentialJiang, B.-F., Hou, D., & Li, J. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.074026 · Cited by 19
Hard dilepton production from a weakly magnetized hot QCD medium
Das, A., Haque, N., Mustafa, M. G., et al. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.094022 · Cited by 19
Partition function for a mass dimension one fermionic field and the dark matter halo of galaxies
Pereira, S. H., & Costa, R. S. (2019) · Modern Physics Letters A · doi:10.1142/s0217732319501268 · Cited by 19
Gravitational waves from breaking of an extra U(1) in SO(10) grand unification
Okada, N., Seto, O., & Uchida, H. (2021) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptab003 · Cited by 19
“[74, 75]).”
Filinov, V. S., Bönitz, M., Ivanov, Y. B., et al. (2015) · Contributions to Plasma Physics · doi:10.1002/ctpp.201400056 · Cited by 19
Arciniega, G., Nettel, F., Ortega, P., & Patiño, L. (2014) · Journal of High Energy Physics · doi:10.1007/jhep04(2014)192 · Cited by 25
“The differential photon production is given by [17, 19, 53] dΓ d~k = e2 (2π)32|~k| Φ(k) ∑”
Photon production of axionic cold dark matter
Lee, D.-S., & Ng, K. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.085003 · Cited by 20
Refractive index of light in the quark-gluon plasma with the hard-thermal-loop perturbation theory
Liu, J., Luo, M. J., Wang, Q., & Xu, H. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.125027 · Cited by 18
Kohyama, H. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.77.045016 · Cited by 19
Islam, C. A., Bandyopadhyay, A., Roy, P. K., et al. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.094028 · Cited by 19
Retarded Green’s functions and forward scattering amplitudes in thermal field theory
Brandt, F. T., Das, A., Frenkel, J., et al. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.59.065004 · Cited by 19
X(3872) , X(4014) , and their bottom partners at finite temperature
Montaña, G., Ramos, A., Tolós, L., et al. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.054014 · Cited by 18
“We note that, in the ITF formalism, thermal corrections enter in loop diagrams [82, 83], and therefore the tree-level interactions at finite temperature remain the same as in vacuum.”
Harada, M., & Nemoto, Y. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.014004 · Cited by 18
Thermal behaviors of light scalar resonances at low temperatures
Gao, R., Guo, Z.-H., & Pang, J.-Y. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.100.114028 · Cited by 18
Medium effects on the electrical and Hall conductivities of a hot and magnetized pion gas
Kalikotay, P., Ghosh, S., Chaudhuri, N., et al. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.076007 · Cited by 18
“[56] M.”
MethodPossible ferromagnetism in the large Nc and Nf limit of quark matter
Ohnishi, K., Makoto Oka, A., & Yasui, S. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.097501 · Cited by 18
Probing strongly coupled anisotropic plasmas from higher curvature gravity
Jahnke, V., & Misobuchi, A. S. (2016) · The European Physical Journal C · doi:10.1140/epjc/s10052-016-4153-2 · Cited by 18
“At leading order in e, the number of photons emitted per unit time and unit volume is given by [116] dΓγ d3k “ e 2 p2πq32|~k| Φpkq ηχμνpkq ˇ”
The linear sigma model at a finite isospin chemical potential
Mao, H., Petropoulos, N., & Zhao, W. Q. (2006) · CERN Document Server (European Organization for Nuclear Research) · Cited by 18
Specific heat of normal, degenerate quark matter: Non-Fermi liquid corrections
Boyanovsky, D., & de Vega, H. J. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.63.114028 · Cited by 18
“…from perturbative terms since these will arise from: i) perturbative corrections to the quasiparticle spectral density not included in (2.17) and ii) the contribution from states a distance > M below the Fermi surface, none of which are associated with the breakdown of the Fermi liquid description.”
BackgroundInfluentialBoyanovsky, D., de Vega, H. J., & Simionato, M. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.085007 · Cited by 18
“b) Magnetic and Debye screening masses: We introduce a definition of the magnetic and Debye screening masses out of equilibrium which are the natural extension of that in equilibrium [29,31,32].”
BackgroundGravitational waves from first order phase transitions during inflation
Chialva, D. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.023512 · Cited by 19
Matsubara-Fradkin thermodynamical quantization of Podolsky electrodynamics
Bonin, C. A., & Pimentel, B. M. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.065023 · Cited by 17
Quantum phase transitions in optical lattices beyond the Bogoliubov approximation
Kleinert, H. M., Narzikulov, Z., & Rakhimov, A. (2012) · Physical Review A · doi:10.1103/physreva.85.063602 · Cited by 18
Rebhan, A. K. (2007) · Springer eBooks · doi:10.1007/3-540-45792-5_5 · Cited by 17
Thermal operator representation of finite temperature graphs
Brandt, F. T., Das, A., Espinosa, O., Frenkel, J., & Perez, S. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.72.085006 · Cited by 19
Unstable particles in matter at a finite temperature: The ρ and ω mesons
Alam, J., Sarkar, S., Roy, P. K., Dutta-Roy, B., & Sinha, B. (1999) · Physical Review C · doi:10.1103/physrevc.59.905 · Cited by 17
Supernova bounds on new scalars from resonant and soft emission
Hardy, E., Sokolov, A. V., & Stubbs, H. (2025) · Journal of High Energy Physics · doi:10.1007/jhep04(2025)013 · Cited by 16
Bulk Properties of Strongly Interacting Matter
Leupold, S., Redlich, K., Stephanov, M. A., Andronic, A., Blaschke, D. B., Bluhm, M., Dumitru, A., Fodor, Z., Friman, B. L., Fuchs, C., et al. (2011) · Lecture notes in physics · doi:10.1007/978-3-642-13293-3_3 · Cited by 16
Jet-induced gauge field instabilities in the quark-gluon plasma: A kinetic theory approach
Mannarelli, M., & Manuel, C. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.77.054018 · Cited by 16
“We briefly recall some results of the HTL approach and derive the dispersion laws that describe the evolution of gauge collective modes [20].”
BackgroundMethodInfluentialD-branes as coherent states in the open string channel
Cantcheff, M. B. (2008) · The European Physical Journal C · doi:10.1140/epjc/s10052-008-0603-9 · Cited by 16
Photoproduction and conductivity in dense holographic QCD
Bu, Y. Y. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.026003 · Cited by 16
Magnetic field effect on charged scalar pair creation at finite temperature
Piccinelli, G., & Sánchez, Á. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.076014 · Cited by 16
“According to the imaginary time formalism, once the sum over the Matsubara frequencies is done, one is allowed to make an analytical continuation of the external momentum: iωm → p0 + i [33].”
MethodThermal CFTs in momentum space
Manenti, A. (2020) · Journal of High Energy Physics · doi:10.1007/jhep01(2020)009 · Cited by 24
“See also [24, 25].”
Soft contribution to the damping rate of a hard photon in a weakly magnetized hot medium
Ghosh, R., Karmakar, B., & Mustafa, M. G. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.056007 · Cited by 16
Bento, B. V., Chakraborty, D., Parameswaran, S., & Zavala, I. (2020) · Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019) · doi:10.22323/1.376.0123 · Cited by 25
Hsiang, J.-T., & Hu, B. L. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.065001 · Cited by 16
One-loop constituent quark contributions to the vector and axial-vector meson curvature mass
Kovács, G., Kovács, P., & Szép, Z. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.056013 · Cited by 16
Medium effects on the relaxation of dissipative flows in a hot pion gas
Mitra, S., Gangopadhyaya, U., & Sarkar, S. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.91.094012 · Cited by 16
Symmetry nonrestoration in a Gross-Neveu model with a random chemical potential
Hong, S.-I., & Kogut, J. B. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.63.085014 · Cited by 16
Scalar quantum field theory in disordered media
Arias, E., Goulart, É., Krein, G. I., Menezes, G., & Svaiter, N. F. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.125022 · Cited by 17
Thermal mass and dispersion relations of quarks in the deconfined phase of quenched QCD
Kaczmarek, O., Karsch, F., Kitazawa, M., et al. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.036006 · Cited by 16
Relaxing near the critical point
Boyanovsky, D., de Vega, H. J., & Simionato, M. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.63.045007 · Cited by 16
Gluon effects on the equation of state of color superconducting strange stars
Ferrer, E. J., de la Incera, V., & Paulucci, L. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.92.043010 · Cited by 16
Production of heavy sterile neutrinos from vector boson decay at electroweak temperatures
Lello, L., Boyanovsky, D., & Pisarski, R. D. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.95.043524 · Cited by 16
Mehr, S. M. A. T., & Sadooghi, N. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.076022 · Cited by 16
Divergences in real-time classical field theories at nonzero temperature
Gert Aarts, A., Nauta, B. J., & van Weert, C. G. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.105002 · Cited by 16
“expressions [16, 17, 18], which introduce linear divergences in the classical theory [3, 4, 5].”
BackgroundQuasi-Particle Description of Strongly Interacting Matter: Towards a FoundationPreprint
Bluhm, M., Kämpfer, B., Schulze, R., & Seipt, D. (2006) · Cited by 16
Satapathy, S., Ghosh, S., & Ghosh, S. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.036006
Debye screening in generalized quantum electrodynamics
Bonin, C. A., Gracia, G., Nogueira, A. A., et al. (2020) · International Journal of Modern Physics A · doi:10.1142/s0217751x20501791 · Cited by 15
Chiral symmetry restoration in a rotating medium
Gaspar, I. I., Hernández, L. A., & Zamora, R. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.094020 · Cited by 15
Originally asymmetric dark matter
Okada, N., & Seto, O. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.063525 · Cited by 15
Czajka, A., & Mrówczyński, S. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.025017 · Cited by 15
Influence of QED Corrections on the Orientation of Chiral Symmetry Breaking in the NJL Model
Fujihara, T., Inagaki, T., & Kimura, D. (2007) · Progress of Theoretical Physics · doi:10.1143/ptp.117.139 · Cited by 15
Nonlocal Nambu–Jona-Lasinio model with a fractional Lorentzian regulator in the real time formalism
Loewe, M., Marquez, F., & Villavicencio, C. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.88.056004 · Cited by 15
Andreoli, M., Bonati, C., D’Elia, M., et al. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.054515 · Cited by 15
Warm inflation, neutrinos and dark matter: a minimal extension of the Standard Model
Levy, M., Rosa, J. G., & Ventura, L. B. (2020) · Journal of High Energy Physics · doi:10.1007/jhep12(2021)176 · Cited by 12
“y 2. Using the nite-temperature propagators ( p) = i p2 m2 + i" = iP 1 p2 m2 + ˇ(p2 m2); (B.21) where P(x) is the Cauchy principal value. The real and imaginary parts of the propagators are [111]: G(11)(k) = iP 1 k2 + 2ˇ(k2)(1=2 + n B(k)) ; S(11)(k) = iP 1 k2 + 2ˇ(k2)(1=2 n F(k)) =k; (B.22) { 34 { for massless pa…”
meson propagation in dense nuclear matter and collective excitations
Dutt-Mazumder, A. K. (2003) · Nuclear Physics A · doi:10.1016/s0375-9474(02)01297-6 · Cited by 15
“This is related to the Debye screening mass as Ω(2) = 23m 2 D [15,16].”
BackgroundHan, C., Hou, D., Jiang, B.-F., et al. (2017) · The European Physical Journal A · doi:10.1140/epja/i2017-12400-9 · Cited by 15
TASI lectures on Phase Transitions, Baryogenesis, and Gravitational Waves
Croon, D. L. (2024) · doi:10.22323/1.439.0003 · Cited by 21
“Since this is a brief overview only, if you are interested in learning more about finite temperature field theory you are encouraged to consider these works (or others such as [7, 8]), as well as the research articles cited in the text.”
BackgroundParticle shells from relativistic bubble walls
Baldes, I., Dichtl, M., Gouttenoire, Y., & Sala, F. (2024) · Journal of High Energy Physics · doi:10.1007/jhep07(2024)231 · Cited by 22
Examination of the Gunion-Bertsch formula for soft gluon radiation
Bhattacharyya, T., Mazumder, S., Das, S. K., et al. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.034033 · Cited by 14
Carlomagno, J. P. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.094012 · Cited by 14
Damping rate of a fermion in ultradegenerate chiral matter
Carignano, S., & Manuel, C. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.096022 · Cited by 14
Measuring chiral imbalance with collisional energy loss
Carignano, S., & Manuel, C. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.116002 · Cited by 14
Spectral and Transport Properties from Lattice QCD
Kaczmarek, O., & Shu, H.-T. (2022) · Lecture notes in physics · doi:10.1007/978-3-030-95491-8_8 · Cited by 14
Analytical approach for the Mott transition in the Kane-Mele-Hubbard model
Hutchinson, J., Klein, P. W., & Hur, K. L. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.075120 · Cited by 14
“It is divergent, but this divergence is not physical and is easily regularized [4].”
BackgroundDadić, I. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.63.025011 · Cited by 14
“1 Introduction Out of equilibrium thermal field theory [1, 2] has recently attracted considerable interest [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15].”
BackgroundPlasma wave instabilities induced by neutrinos
Bento, L. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.013004 · Cited by 14
“In the real-time formalism [12, 13, 14], adopted here, the electron propagator in a homogeneous and unpolarized plasma is given by (p/+m) [ i p2 −m2 − 2π δ(p 2 −m2) ( θ(p0)fe(p) + θ(−p0)fē(−p) ) ] , (2) where fe, fē are the electron and positron distribution functions respectively.”
MethodSize effects on the thermodynamic behavior of a simplified generalized scalar Yukawa model
Abreu, L. M., Nery, E. S., & Malbouisson, A. P. C. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.91.087701 · Cited by 14
Simple out-of-equilibrium field theory formalism?
Gelis, F., Schiff, D., & Serreau, J. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.64.056006 · Cited by 14
Thermal operator representation of finite temperature graphs. II.
Brandt, F. T., Das, A., Espinosa, O., Frenkel, J., & Perez, S. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.73.065010 · Cited by 15
Thermal operator representation for Matsubara sums
Espinosa, O. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.71.065009 · Cited by 14
Ultrasoft fermionic excitation at finite chemical potential
Blaizot, J.-P., & Satow, D. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.89.096001 · Cited by 13
Gómez, A., von Dossow, R. M., Martín-Ruiz, A., & Urrutia, L. F. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.065005 · Cited by 15
Satow, D., Hidaka, Y., & Kunihiro, T. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.045017 · Cited by 13
“2 The fermion propagator G ð p Þ in the imaginary time formalism [15,16] is expressed with the self-energy (cid”
MethodStructure of a thermal quasifermion in the QCD/QED medium
Nakkagawa, H., Yokota, H., & Yoshida, K. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.096007 · Cited by 13
Electromagnetic effects in the pion dispersion relation at finite temperature
Nicola, Á. G., & Andrés, R. T. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.89.116009 · Cited by 13
Charged-particle decay at finite temperature
Czarnecki, A., Kamionkowski, M., Lee, S. K., et al. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.025018 · Cited by 13
String entanglement and D-branes as pure states
Cantcheff, M. B. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.046001 · Cited by 13
Out-of-equilibrium electromagnetic radiation
Serreau, J. (2003) · CERN Document Server (European Organization for Nuclear Research) · Cited by 13
Nonequilibrium Field Theory Description of the Bose-Einstein Condensate
Barci, D. G., Fraga, E. S., & Ramos, R. O. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.479 · Cited by 13
Thermal fluctuations of induced fermion number
Dunne, G. V., & Rao, K. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.64.025003 · Cited by 13
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
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