Advances in perturbative thermal field theory - Ultra-relativistic ...

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352 U Kraemmer and A Rebhan Contents Page 1. Introduction 354 1.1. Outline 354 2. Basics 355 2.1. Imaginary-time (Matsubara) formalism 357 2.2. Real-time (Keldysh) formalism 358 2.3. Extension to gauge theories 360 3. Resummation issues in scalar φ 4 -theory 362 3.1. Daisy and foam resummation 362 3.2. Thermal masses 363 3.3. Perturbation series 364 3.4. Dimensional reduction 364 3.5. Apparent convergence 365 3.6. Restoration of spontaneously broken symmetry 368 4. QCD thermodynamics 369 4.1. Dimensional reduction 369 4.2. Apparent convergence 371 4.3. Finite chemical potential 374 4.4. Low temperatures and high chemical potentials 375 5. The quasi-particle spectrum in gauge theories 376 5.1. Gauge-boson propagator 377 5.1.1. Gauge independence of singularities 379 5.1.2. Gauge-field quasi-particles at leading order 379 5.2. Fermions 381 5.3. Diquark condensates and colour superconductivity 383 6. HTL effective action and resummation 385 6.1. HTL effective action 385 6.2. Kinetic-theory approach 386 6.3. HTL /HDL resummation 387 6.3.1. HTL-screened perturbation theory (HTLPT) 388 6.3.2. HTL resummed thermodynamics through -derivable approximations 388 7. Next-to-leading order corrections to the quasi-particle spectrum 391 7.1. Long-wavelength plasmon damping 392 7.2. NLO correction to the plasma frequency 393 7.3. NLO correction to the Debye mass 393 7.3.1. Non-perturbative definitions of the Debye mass 396 7.4. Magnetostatic screening 397 7.5. Dynamical screening and damping at high temperatures 397 7.6. Damping of high-momentum fermions in a degenerate plasma 400 7.7. Non-Fermi-liquid contributions to the real part of the fermion self-energy 400 7.8. NLO corrections to real parts of dispersion laws at high temperatures 401
Thermal field theory 353 7.8.1. Energetic quarks and transverse gluons 402 7.8.2. Longitudinal plasmons 402 8. Resummations beyond HTLs 404 8.1. Ultrasoft amplitudes 404 8.2. Light-like external momenta 405 8.3. Transport coefficients 406 9. HTLs and gravity 406 9.1. HTL gravitational polarization tensor 407 9.2. Self-consistent cosmological perturbations from thermal field theory 409 9.2.1. Purely collisionless matter 409 9.2.2. Weak self-interactions and HTL resummation 411 10. Conclusions 412 Appendix 413 A. Spectral representation of HTL/HDL propagators 413 A.1. Gauge-boson propagator 413 A.2. Fermion propagator 415 Acknowledgments 416 References 416
Page 1: INSTITUTE OF PHYSICS PUBLISHING Rep
Page 5 and 6: Thermal field theory 355 the thermo
Page 7 and 8: Thermal field theory 357 It is of c
Page 9 and 10: Thermal field theory 359 close rela
Page 11 and 12: Thermal field theory 361 Hilbert su
Page 13 and 14: Thermal field theory 363 Figure 3.
Page 15 and 16: Thermal field theory 365 where φ 0
Page 17 and 18: Thermal field theory 367 where tr d
Page 19 and 20: Thermal field theory 369 m eff ( ¯
Page 21 and 22: Thermal field theory 371 determined
Page 25 and 26: Thermal field theory 375 4.4. Low t
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Page 37 and 38: Thermal field theory 387 equations
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Page 45 and 46: Thermal field theory 395 where ˜µ
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Thermal field theory 403 Figure 14.
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Thermal field theory 405 Figure 16.
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Thermal field theory 407 In the phy
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Thermal field theory 409 9.2. Self-
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Thermal field theory 411 (a) (b) Fi
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Thermal field theory 413 picture, o
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Thermal field theory 415 obtained b
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Thermal field theory 417 [22] Keldy
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Thermal field theory 419 [87] Baym
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Thermal field theory 421 [149] Poly
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Thermal field theory 423 [212] Rebh
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Thermal field theory 425 [278] Gerh
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Thermal field theory 427 [342] Buch
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Thermal field theory 429 [401] Flec
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Thermal field theory 431 [462] Krae
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