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Author Hakim, Rémi, 1936-
Title Introduction to relativistic statistical mechanics : classical and quantum / Rémi Hakim.
Imprint Hackensack, NJ : World Scientific, ©2011.

Author Hakim, Rémi, 1936-
Subject Statistical mechanics.
Relativistic quantum theory.
Relativistic kinematics.
Description 1 online resource (xxvii, 538 pages) : illustrations
Bibliography Note Includes bibliographical references (pages 465-528) and index.
Note Print version record.
Contents 1. The one-Particle relativistic distribution function. 1.1. The one-particle relativistic distribution function. 1.2. The Juttner-Synge equilibrium distribution. 1.3. From the microcanonical distribution. 1.4. Equilibrium fluctuations. 1.5. One-particle Liouville theorem. 1.6. The relativistic rotating gas -- 2. Relativistic kinetic theory and the BGK equation. 2.1. Relativistic hydrodynamics. 2.2. The relaxation time approximation. 2.3. The relativistic kinetic theory approach to hydrodynamics. 2.4. The static conductivity tensor. 2.5. Approximation methods for the relativistic Boltzmann equation and other kinetic equations. 2.6. Transport coefficients for a system embedded in a magnetic field -- 3. Relativistic plasmas. 3.1. Electromagnetic quantities in covariant form. 3.2. The static conductivity tensor. 3.3. Debye-Huckel law. 3.4. Derivation of the plasma modes. 3.5. Brief discussion of the plasma modes. 3.6. The conductivity tensor. 3.7. Plasma-beam instability -- 4. Curved space-time and cosmology. 4.1. Basic modifications. 4.2. Thermal equilibrium in a gravitational field. 4.3. Einstein-Vlasov equation. 4.4. An illustration in cosmology. 4.5. Cosmology and relativistic kinetic theory -- 5. Relativistic statistical mechanics. 5.1. The dynamical problem. 5.2. Statement of the main statistical problems. 5.3. Many-particle distribution functions. 5.4. The relativistic BBGKY hierarchy. 5.5. Self-interaction and radiation. 5.6. Radiation quantities. 5.7. A few relativistic kinetic equations. 5.8. Statistics of fields and particles -- 6. Relativistic stochastic processes and related questions. 6.1. Stochastic processes in Minkowski space-time. 6.2. Stochastic processes in [symbol] space. 6.3. Relativistic Brownian motion. 6.4. Random gravitational fields : An open problem -- 7. The density operator. 7.1. The density operator for thermal equilibrium. 7.2. Relativistic bosons in thermal equilibrium. 7.3. Free fermions in thermal equilibrium. 7.4. Thermodynamic properties of the relativistic ideal Fermi-Dirac gas. 7.5. White dwarfs : The degenerate electron gas. 7.6. Functional representation of the partition function.
8. The covariant Wigner function. 8.1. The covariant Wigner function for spin 1/2 particles. 8.2. Equilibrium fluctuations of fermions. 8.3. A simple example. 8.4. The BBGKY relativistic quantum hierarchy. 8.5. Perturbation expansion of the Wigner function. 8.6. The Wigner function for bosons. 8.7. Gauge properties of the Wigner function -- 9. Fermions interacting via a scalar field : A simple example. 9.1. Thermal equilibrium. 9.2. Collective modes. 9.3. Two-body correlations. 9.4. Renormalization -- An illustration of the procedure. 9.5. Qualitative discussion of the effects of renormalization. 9.6. Thermodynamics of the system. 9.7. Renormalization of the excitation spectrum. 9.8. A short digression on bosons -- 10. Covariant kinetic equations in the quantum domain. 10.1. General form of the kinetic equation. 10.2. An introductory example. 10.3. A general relaxation time approximation -- 11. Application to nuclear matter. 11.1. Thermodynamic properties at finite temperature. 11.2. Remarks on the oscillation spectra of mesons. 11.3. Transport coefficients of nuclear matter. 11.4. Discussion. 11.5. Dense nuclear matter : Neutron stars -- 12. Strong magnetic fields. 12.1. Relations obeyed by the magnetic field. 12.2. The partition function. 12.3. Relativistic quantum Liouville equation. 12.4. The equilibrium Wigner function for noninteracting electrons. 12.5. The Wigner function of the ideal magnetized electron gas. 12.6. The magnetized vacuum. 12.7. Fluctuations. 12.8. Polarization tensors of the magnetized electron gas and of the magnetized vacuum. 12.9. Remarks on the transport coefficients of the magnetized electron gas. 12.10. Astrophysical aspects -- 13. Statistical mechanics of relativistic quasiparticles. 13.1. Classical fields. 13.2. Quantum quasiparticles. 13.3. Problems with the quantization of quasiparticles. 13.4. The covariant Wigner function. 13.5. Equilibrium properties. 13.6. A simple example : The [symbol] model. 13.7. Remarks on the thermodynamics of quasiparticles. 13.8. Equilibrium fluctuations. 13.9. Remarks on the negative energy modes. 13.10. Interacting quasibosons -- 14. The relativistic Fermi liquid. 14.1. Independent quasifermions. 14.2. Interacting quasifermions. 14.3. Kinetic equation for quasiparticles. 14.4. Remarks on the relativistic Landau theory -- 15. The QED plasma. 15.1. Basic equations. 15.2. Plasma collective modes. 15.3. The fluctuation-dissipation theorem and its inverse. 15.4. Four-current fluctuations and the polarization tensor. 15.5. The polarization tensor at order e[symbol]. 15.6. Quasiparticles in the relativistic plasma.
Summary This is one of the very few books focusing on relativistic statistical mechanics, and is written by a leading expert in this special field. It started from the notion of relativistic kinetic theory, half a century ago, exploding into relativistic statistical mechanics. This will interest specialists of various fields, especially the (classical and quantum) plasma physics. However, quantum physics - to which a major part is devoted - will be of more interest since, not only it applies to quantum plasma physics, but also to nuclear matter and to strong magnetic field, cosmology, etc. Although the domain of gauge theory is not covered in this book, the topic is not completely forgotten, in particular in the domain of plasma physics. This book is particularly readable for graduate students and a fortiori to young researchers for whom it offers methods and also appropriate schemes to deal with the current problems encountered in astrophysics, strong magnetic, nuclear or even in high energy physics.
Note English.
ISBN 9789814322454 (electronic bk.)
9814322458 (electronic bk.)
OCLC # 755590064
Additional Format Print version: Hakim, Rémi, 1936- Introduction to relativistic statistical mechanics. Hackensack, NJ : World Scientific, ©2011 9789814322430 (DLC) 2010054042 (OCoLC)639159318

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