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E-raamat: Introduction to Relativistic Statistical Mechanics: Classical and Quantum [World Scientific e-raamat]

(Paris-meudon Observatory, France)
  • Formaat: 568 pages
  • Ilmumisaeg: 07-Apr-2011
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789814322454
Teised raamatud teemal:
  • World Scientific e-raamat
  • Hind: 111,80 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Introduction to Relativistic Statistical Mechanics: Classical and QuantumSuurem pilt
  • Formaat: 568 pages
  • Ilmumisaeg: 07-Apr-2011
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789814322454
Teised raamatud teemal:
World Scientific e-raamatudRohkem infot World Scientific e-raamatute kohta
Raamatu kodulehekülg: http://www.worldscientific.com/worldscibooks/10.1142/7881#t=toc
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, in strong magnetic, in nuclear or even in high energy physics.
Preface xvii
Notations and Conventions xix
Introduction xxi
1 The One-Particle Relativistic Distribution Function
1(26)
1.1 The One-Particle Relativistic Distribution Function
1(5)
1.1.1 The phase space "volume element"
5(1)
1.2 The Juttner--Synge Equilibrium Distribution
6(10)
1.2.1 Thermodynamics of the Juttner--Synge gas
9(1)
1.2.2 Thermal velocity
10(2)
1.2.3 Moments of the Juttner--Synge function
12(1)
1.2.4 Orthogonal polynomials
13(2)
1.2.5 Zero mass particles
15(1)
1.3 From the Microcanonical Distribution to the Juttner--Synge One
16(3)
1.4 Equilibrium Fluctuations
19(2)
1.5 One-Particle Liouville Theorem
21(3)
1.5.1 Relativistic Liouville equation from the Hamiltonian equations of motion
22(2)
1.5.2 Conditions for the Juttner--Synge functions to be an equilibrium
24(1)
1.6 The Relativistic Rotating Gas
24(3)
2 Relativistic Kinetic Theory and the BGK Equation
27(20)
2.1 Relativistic Hydrodynamics
29(6)
2.1.1 Sound velocity
31(1)
2.1.2 The Eckart approach
32(2)
2.1.3 The Landau--Lifschitz approach
34(1)
2.2 The Relaxation Time Approximation
35(1)
2.3 The Relativistic Kinetic Theory Approach to Hydrodynamics
36(4)
2.4 The Static Conductivity Tensor
40(1)
2.5 Approximation Methods for the Relativistic Boltzmann Equation and Other Kinetic Equations
41(2)
2.5.1 A simple Chapman--Enskog approximation
42(1)
2.6 Transport Coefficients for a System Embedded in a Magnetic Field
43(4)
3 Relativistic Plasmas
47(20)
3.1 Electromagnetic Quantities in Covariant Form
47(3)
3.2 The Static Conductivity Tensor
50(1)
3.3 Debye--Huckel Law
51(1)
3.4 Derivation of the Plasma Modes
52(5)
3.4.1 Evaluation of the various integrals
55(1)
3.4.2 Collective modes in extreme cases
56(1)
3.5 Brief Discussion of the Plasma Modes
57(5)
3.6 The Conductivity Tensor
62(1)
3.7 Plasma--Beam Instability
63(4)
3.7.1 Perturbed dispersion relations for the plasma--beam system
63(1)
3.7.2 Stability of the beam--plasma system
64(3)
4 Curved Space--Time and Cosmology
67(27)
4.1 Basic Modifications
68(2)
4.2 Thermal Equilibrium in a Gravitational Field
70(1)
4.2.1 Thermal equilibrium in a static isotropic metric
71(1)
4.3 Einstein--Vlasov Equation
71(5)
4.3.1 Linearization of Einstein's equation
72(2)
4.3.2 The formal solution to the linearized Einstein equation
74(2)
4.3.3 The self-consistent kinetic equation for the gravitating gas
76(1)
4.4 An Illustration in Cosmology
76(5)
4.4.1 The two-timescale approximation
78(2)
4.4.2 Derivation of the dispersion relations (a rough outline)
80(1)
4.5 Cosmology and Relativistic Kinetic Theory
81(13)
4.5.1 Cosmology: a very brief overview
82(3)
4.5.2 Kinetic theory and cosmology
85(2)
4.5.3 Kinetic theory of the observed universe
87(1)
4.5.4 Statistical mechanics in the primeval universe
88(2)
4.5.5 Particle survival
90(4)
5 Relativistic Statistical Mechanics
94(34)
5.1 The Dynamical Problem
94(2)
5.2 Statement of the Main Statistical Problems
96(6)
5.2.1 The initial value problem: observations and measures
97(3)
5.2.2 Phase space and the Gibbs ensemble
100(2)
5.3 Many-Particle Distribution Functions
102(3)
5.3.1 Statistics of the particles' manifolds
103(2)
5.4 The Relativistic BBGKY Hierarchy
105(4)
5.4.1 Cluster decomposition of the relativistic distribution functions
107(2)
5.5 Self-interaction and Radiation
109(7)
5.5.1 An alternative treatment of radiation reaction
111(2)
5.5.2 Remarks on irreversibility
113(1)
5.5.3 Remarks on thermal equilibrium
114(2)
5.6 Radiation Quantities
116(2)
5.7 A Few Relativistic Kinetic Equations
118(7)
5.7.1 Derivation of the covariant Landau equation
118(3)
5.7.2 The relativistic Vlasov equation with radiation effects
121(3)
5.7.3 Radiation effects for a relativistic plasma in a magnetic field
124(1)
5.8 Statistics of Fields and Particles
125(3)
6 Relativistic Stochastic Processes and Related Questions
128(24)
6.1 Stochastic Processes in Minkowski Space---Time
129(4)
6.1.1 Basic definitions
130(1)
6.1.2 Conditional currents
131(1)
6.1.3 Markovian processes in space---time
131(2)
6.2 Stochastic Processes in μ Space
133(9)
6.2.1 An overview
134(1)
6.2.2 Markovian processes
135(2)
6.2.3 An alternative approach
137(2)
6.2.4 Markovian processes
139(1)
6.2.5 A simple illustration
140(2)
6.3 Relativistic Brownian Motion
142(2)
6.4 Random Gravitational Fields: An Open Problem
144(8)
6.4.1 A simple example
148(1)
6.4.2 The case of thermal equilibrium
149(1)
6.4.3 Matter-induced fluctuations
150(1)
6.4.4 Random Einstein equations
151(1)
7 The Density Operator
152(42)
7.1 The Density Operator for Thermal Equilibrium
153(6)
7.1.1 Thermodynamic properties
154(2)
7.1.2 The partition function of the relativistic ideal gas
156(2)
7.1.3 The average occupation number
158(1)
7.2 Relativistic Bosons in Thermal Equilibrium
159(12)
7.2.1 The complex scalar field
161(3)
7.2.2 Charge fluctuations
164(1)
7.2.3 A few remarks on the calculation of various integrals
164(1)
7.2.4 Bose--Einstein condensation
165(2)
7.2.5 Interactions
167(4)
7.3 Free Fermions in Thermal Equilibrium
171(3)
7.4 Thermodynamic Properties of the Relativistic Ideal Fermi--Dirac Gas
174(7)
7.4.1 Remarks on the numerical calculations of various physical quantities
175(1)
7.4.2 The degenerate Fermi gas
175(2)
7.4.3 Thermal corrections: Sommerfeld expansion
177(2)
7.4.4 Corrections for various thermodynamic quantities
179(1)
7.4.5 High temperature expansion (nondegenerate)
180(1)
7.5 White Dwarfs: The Degenerate Electron Gas
181(6)
7.5.1 Cooling of white dwarfs
185(2)
7.5.2 Pycnonuclear reactions
187(1)
7.6 Functional Representation of the Partition Function
187(7)
7.6.1 The partition function for gauge particles (photons)
188(1)
7.6.2 The photons' partition function
189(2)
7.6.3 Illustration in the case of the Lorentz gauge
191(3)
8 The Covariant Wigner Function
194(34)
8.1 The Covariant Wigner Function for Spin 1/2 Particles
195(9)
8.1.1 Basic equations
197(3)
8.1.2 The equilibrium Wigner function for free fermions
200(1)
8.1.3 Polarized media
201(3)
8.2 Equilibrium Fluctuations of Fermions
204(3)
8.3 A Simple Example
207(1)
8.4 The BBGKY Relativistic Quantum Hierarchy
208(3)
8.5 Perturbation Expansion of the Wigner Function
211(2)
8.6 The Wigner Function for Bosons
213(5)
8.6.1 The example of the λφ4 theory
216(1)
8.6.2 Four-current fluctuations of the complex scalar field
217(1)
8.7 Gauge Properties of the Wigner Function
218(10)
8.7.1 Gauge-invariant Wigner functions
218(4)
8.7.2 A few remarks
222(1)
8.7.3 Gauge-invariant Wigner functions for the photon field
223(2)
8.7.4 Another gauge-invariant Wigner function
225(1)
8.7.5 Gauge invariance and approximations
226(2)
9 Fermions Interacting via a Scalar Field: A Simple Example
228(34)
9.1 Thermal Equilibrium
229(4)
9.2 Collective Modes
233(1)
9.3 Two-Body Correlations
234(6)
9.3.1 A brief discussion
237(1)
9.3.2 Exchange correlations
238(2)
9.4 Renormalization --- An Illustration of the Procedure
240(6)
9.4.1 Regularization of the gap equation
241(3)
9.4.2 Regularization of the energy--momentum tensor
244(1)
9.4.3 Determination of the constants (AF, BF, CF, DF)
245(1)
9.5 Qualitative Discussion of the Effects of Renormalization
246(3)
9.6 Thermodynamics of the System
249(4)
9.6.1 The gap equation as a minimum of the free energy
250(1)
9.6.2 Thermodynamics
251(2)
9.7 Renormalization of the Excitation Spectrum
253(5)
9.7.1 Comparison with the semiclassical case
257(1)
9.8 A Short Digression on Bosons
258(4)
10 Covariant Kinetic Equations in the Quantum Domain
262(15)
10.1 General Form of the Kinetic Equation
264(1)
10.2 An Introductory Example
265(4)
10.3 A General Relaxation Time Approximation
269(8)
10.3.1 Properties of the kinetic system
270(2)
10.3.2 The collision term
272(2)
10.3.3 General form of F(1)
274(3)
11 Application to Nuclear Matter
277(32)
11.1 Thermodynamic Properties at Finite Temperature
279(6)
11.1.1 Thermodynamics in some important cases
282(3)
11.2 Remarks on the Oscillation Spectra of Mesons
285(1)
11.3 Transport Coefficients of Nuclear Matter
286(13)
11.3.1 Chapman--Enskog expansion
288(2)
11.3.2 Transport coefficients: Eckart versus Landau--Lifschitz representations
290(3)
11.3.3 Entropy production
293(4)
11.3.4 A brief comparison: BGK versus BUU
297(2)
11.4 Discussion
299(3)
11.5 Dense Nuclear Matter: Neutron Stars
302(7)
11.5.1 The static equilibrium of a neutron star
303(1)
11.5.2 The composition of matter in a neutron star
304(3)
11.5.3 Beyond the drip point
307(2)
12 Strong Magnetic Fields
309(47)
12.1 Relations Obeyed by the Magnetic Field
312(2)
12.2 The Partition Function
314(5)
12.2.1 Magnetization of an electron gas
317(2)
12.3 Relativistic Quantum Liouville Equation
319(5)
12.3.1 Solution of the inhomogeneous equation
321(2)
12.3.2 The initial value problem
323(1)
12.4 The Equilibrium Wigner Function for Noninteracting Electrons
324(2)
12.4.1 Thermodynamic quantities
325(1)
12.5 The Wigner Function of the Ideal Magnetized Electron Gas
326(10)
12.5.1 The nonmagnetic field limit
328(1)
12.5.2 Equations of state
329(1)
12.5.3 Is the pressure isotropic?
330(1)
12.5.4 The completely degenerate case
331(2)
12.5.5 Magnetization
333(2)
12.5.6 Landau orbital ferromagnetism: LOFER states
335(1)
12.6 The Magnetized Vacuum
336(4)
12.6.1 The general structure of the vacuum Wigner function
336(2)
12.6.2 The Wigner function of the magnetized vacuum
338(1)
12.6.3 Renormalization of the vacuum Wigner function
339(1)
12.7 Fluctuations
340(8)
12.7.1 Fluctuations of the four-current
341(7)
12.8 Polarization Tensors of the Magnetized Electron Gas and of the Magnetized Vacuum
348(2)
12.8.1 The vacuum polarization tensor
349(1)
12.9 Remarks on the Transport Coefficients of the Magnetized Electron Gas
350(3)
12.10 Astrophysical Aspects
353(3)
13 Statistical Mechanics of Relativistic Quasiparticles
356(44)
13.1 Classical Fields
359(11)
13.1.1 Internal symmetries and conserved currents
360(3)
13.1.2 Space--time symmetries
363(4)
13.1.3 A general remark
367(3)
13.2 Quantum Quasiparticles
370(4)
13.2.1 Formal quantization
371(3)
13.3 Problems with the Quantization of Quasiparticles
374(5)
13.3.1 A first example
374(2)
13.3.2 Another example the QED plasma
376(1)
13.3.3 Migdal's approach
377(2)
13.4 The Covariant Wigner Function
379(3)
13.5 Equilibrium Properties
382(3)
13.6 A Simple Example: The λφ4 Model
385(3)
13.7 Remarks on the Thermodynamics of Quasiparticles
388(3)
13.8 Equilibrium Fluctuations
391(3)
13.9 Remarks on the Negative Energy Modes
394(1)
13.10 Interacting Quasibosons
395(5)
13.10.1 The long wavelength and low frequency limit
398(2)
14 The Relativistic Fermi Liquid
400(22)
14.1 Independent Quasifermions
400(7)
14.1.1 Quantization and observables
402(3)
14.1.2 Statistical expressions
405(1)
14.1.3 Thermal equilibrium
406(1)
14.2 Interacting Quasifermions
407(3)
14.2.1 The long wavelength and low frequency limit
409(1)
14.3 Kinetic Equation for Quasiparticles
410(2)
14.4 Remarks on the Relativistic Landau Theory
412(10)
15 The QED Plasma
422(24)
15.1 Basic Equations
422(1)
15.2 Plasma Collective Modes
423(5)
15.3 The Fluctuation--Dissipation Theorem and Its Inverse
428(1)
15.4 Four-Current Fluctuations and the Polarization Tensor
429(4)
15.5 The Polarization Tensor at Order e2
433(3)
15.6 Quasiparticles in the Relativistic Plasma
436(10)
15.6.1 Quasiphotons in thermal equilibrium
436(4)
15.6.2 Gauge properties
440(2)
15.6.3 Quasielectron modes in thermal equilibrium
442(4)
Appendix A A Few Useful Properties of Some Special Functions
446(2)
A.1 Kelvin's Functions
446(1)
A.2 Associated Laguerre Polynomials
447(1)
Appendix B γ Matrices
448(3)
Appendix C Outline of Functional Methods
451(6)
C.1 Functional Differentiation
452(1)
C.2 Functional Integration
453(4)
Appendix D Units
457(3)
D.1 Ordinary Units
457(1)
D.2 Other Units of Interest
458(2)
Appendix E Some Useful Formulae for Wigner Functions
460(5)
E.1 Useful Formulae for Bosons
460(2)
E.2 Useful Formulae for Fermions
462(3)
Bibliography 465(64)
Index 529
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