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 465528) and index. 
Note 
Print version record. 
Contents 
1. The oneParticle relativistic distribution function. 1.1. The oneparticle relativistic distribution function. 1.2. The JuttnerSynge equilibrium distribution. 1.3. From the microcanonical distribution. 1.4. Equilibrium fluctuations. 1.5. Oneparticle 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. DebyeHuckel law. 3.4. Derivation of the plasma modes. 3.5. Brief discussion of the plasma modes. 3.6. The conductivity tensor. 3.7. Plasmabeam instability  4. Curved spacetime and cosmology. 4.1. Basic modifications. 4.2. Thermal equilibrium in a gravitational field. 4.3. EinsteinVlasov 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. Manyparticle distribution functions. 5.4. The relativistic BBGKY hierarchy. 5.5. Selfinteraction 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 spacetime. 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 FermiDirac 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. Twobody 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 fluctuationdissipation theorem and its inverse. 15.4. Fourcurrent 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.) 

9789814322430 

9814322431 

1283234726 

9781283234726 

9786613234728 

6613234729 
OCLC # 
755590064 
Additional Format 
Print version: Hakim, Rémi, 1936 Introduction to relativistic statistical mechanics. Hackensack, NJ : World Scientific, ©2011 9789814322430 (DLC) 2010054042 (OCoLC)639159318 
