Unified Non-Local Relativistic Theory of Transport Processes highlights the most significant features of non-local relativistic theory, which is a highly effective tool for solving many physical problems in areas where the classical local theory runs into difficulties. The book provides the fundamental science behind new non-local physics – generalized for relativistic cases and applied in a range of scales – from transport phenomena in massless physical systems to unified theory of dissipative structures.
The book complements the author’s previous monograph on Unified Non-Local Theory of Transport Processes (Elsevier, 2015), which is mainly devoted to non-relativistic non-local physics. Nevertheless, the theory as handled in this new work is outlined independently so the book can be studied on its own.
1. Introduction: Review of the Main Principles of the Unified Nonlocal Theory of Transport Processes - p. 1 2. Chapter 1: Hydrodynamic Form of the Dirac Quantum Relativistic Equation - p. 51 3. Abstract - p. 53 4. 1.1 “Derivation” of the Dirac Equation - p. 53 5. 1.2 Hydrodynamic Form of Dirac Equation in the Absence of an External Field - p. 68 6. 1.3 Hydrodynamic Form of the Dirac Equation in an External Electromagnetic Field - p. 77 7. Chapter 2: Generalized Relativistic Nonlocal Kinetic Equation Without Taking Into Account the External Forces - p. 93 8. Chapter 3: Classical Relativistic Equilibrium Distribution Function and Computation of Equilibrium Values of Some Macroscopic Quantities - p. 112 9. Chapter 4: Generalized Relativistic Hydrodynamic Enskog Equations Without Regard to External Forces - p. 127 10. Abstract - p. 129 11. 4.1 Derivation of the Continuity Equation - p. 129 12. 4.2 Derivation of the Motion Equation - p. 135 13. 4.3 Derivation of the Energy Equation - p. 138 14. 4.4 Generalized Enskog System of Relativistic Hydrodynamic Equations - p. 142 15. Chapter 5: Generalized Relativistic Hydrodynamic Euler Equations Without Taking Into Account the External Forces - p. 147 16. Abstract - p. 149 17. 5.1 Components of Tensor Physical Quantities in the Local Rest System - p. 149 18. 5.2 The Lorentz Transformation Law for Tensor Physical Quantities in One-Dimensional Case - p. 153 19. 5.3 Generalized Relativistic Euler Equations for One-Dimensional Motion - p. 157 20. 5.4 Generalized One-Dimensional Nonrelativistic Euler Equations as the Asymptotic Behavior of the Relativistic Equations - p. 159 21. 5.5 Generalized Relativistic Euler Equations for Arbitrary Motion - p. 166 22. 5.6 Generalized Nonrelativistic Euler Equations for an Arbitrary Motion as an Asymptotic Form of the Relativistic Equations - p. 171 23. Chapter 6: The Solution of Some Physical Problems on the Basis of the Nonlocal Relativistic Equations Without Taking Into Account the External Forces - p. 178 24. Abstract - p. 179 25. 6.1 The Propagation of Plane Harmonic Waves of Small Amplitude in the Ultra-Relativistic Medium - p. 179 26. 6.2 Shock Waves in Relativistic Gas - p. 205 27. 6.3 The Collision of Nucleons - p. 221 28. Chapter 7: Nonlocal Relativistic Kinetic Equation and Hydrodynamic Enskog Equations Taking Into Account the External Forces - p. 242 29. Abstract - p. 243 30. 7.1 Nonlocal Relativistic Kinetic Equation Taking Into Account the External Forces - p. 243 31. 7.2 The Derivation of the Continuity Equation - p. 245 32. 7.3 The Derivation of the Motion Equation - p. 249 33. 7.4 The Derivation of the Energy Equation - p. 253 34. 7.5 Generalized System of Relativistic Hydrodynamic Enskog Equations - p. 257 35. 7.6 Generalized System of Relativistic Hydrodynamic Enskog Equations for Multicomponent Mixture - p. 264 36. Chapter 8: Generalized Relativistic Euler Equations Taking Into Account External Forces - p. 270 37. Chapter 9: Application of the Generalized Relativistic Kinetic and Hydrodynamic Equations to the Study of Graphene - p. 283 38. Abstract - p. 285 39. 9.1 Features of the Band Structure of Graphene - p. 285 40. 9.2 Generalized Kinetic and Hydrodynamic Equations for Graphene in an Electric Field - p. 293 41. 9.3 Wave Transfer in Graphene - p. 306 42. 9.4 The Hall Effect in the Relativistic Nonlocal Theory of Massless Particles - p. 321 43. Chapter 10: Application of Relativistic Nonlocal Physics in the Theory of Gravitational Field Interaction With a Laser Beam - p. 352 44. Abstract - p. 353 45. 10.1 Nonlocal Physics and Gravitational Waves - p. 353 46. 10.2 Basic Equations of Relativistic Nonlocal Physics Having Regard to External Forces - p. 354 47. 10.3 Calculation of the Tensor Moments for the Laser Beam Evolution - p. 356 48. 10.4 Nonlocal Relativistic Equations in the Explicit Form - p. 363 49. 10.5 Wave Solutions for GFR-Interaction - p. 377 50. Chapter 11: Application of the Generalized Relativistic Hydrodynamic Equations to the Study of the Interaction of Planck Radiation With the Gravitational Field - p. 390 51. Chapter 12: Connection Between Time Quantization in the Frame of Nonlocal Relativistic Physics and Shannon-Nyquist-Kotelnikov Theorem - p. 410 52. Appendices - p. 429 53. Index - p. 451
Unified Non-Local Relativistic Theory of Transport Processes highlights the most significant features of non-local relativistic theory, which is a highly effective tool for solving many physical problems in areas where the classical local theory runs into difficulties. The book provides the fundamental science behind new non-local physics – generalized for relativistic cases and applied in a range of scales – from transport phenomena in massless physical systems to unified theory of dissipative structures.
The book complements the author’s previous monograph on Unified Non-Local Theory of Transport Processes (Elsevier, 2015), which is mainly devoted to non-relativistic non-local physics. Nevertheless, the theory as handled in this new work is outlined independently so the book can be studied on its own.
1. Introduction: Review of the Main Principles of the Unified Nonlocal Theory of Transport Processes - p. 1 2. Chapter 1: Hydrodynamic Form of the Dirac Quantum Relativistic Equation - p. 51 3. Abstract - p. 53 4. 1.1 “Derivation” of the Dirac Equation - p. 53 5. 1.2 Hydrodynamic Form of Dirac Equation in the Absence of an External Field - p. 68 6. 1.3 Hydrodynamic Form of the Dirac Equation in an External Electromagnetic Field - p. 77 7. Chapter 2: Generalized Relativistic Nonlocal Kinetic Equation Without Taking Into Account the External Forces - p. 93 8. Chapter 3: Classical Relativistic Equilibrium Distribution Function and Computation of Equilibrium Values of Some Macroscopic Quantities - p. 112 9. Chapter 4: Generalized Relativistic Hydrodynamic Enskog Equations Without Regard to External Forces - p. 127 10. Abstract - p. 129 11. 4.1 Derivation of the Continuity Equation - p. 129 12. 4.2 Derivation of the Motion Equation - p. 135 13. 4.3 Derivation of the Energy Equation - p. 138 14. 4.4 Generalized Enskog System of Relativistic Hydrodynamic Equations - p. 142 15. Chapter 5: Generalized Relativistic Hydrodynamic Euler Equations Without Taking Into Account the External Forces - p. 147 16. Abstract - p. 149 17. 5.1 Components of Tensor Physical Quantities in the Local Rest System - p. 149 18. 5.2 The Lorentz Transformation Law for Tensor Physical Quantities in One-Dimensional Case - p. 153 19. 5.3 Generalized Relativistic Euler Equations for One-Dimensional Motion - p. 157 20. 5.4 Generalized One-Dimensional Nonrelativistic Euler Equations as the Asymptotic Behavior of the Relativistic Equations - p. 159 21. 5.5 Generalized Relativistic Euler Equations for Arbitrary Motion - p. 166 22. 5.6 Generalized Nonrelativistic Euler Equations for an Arbitrary Motion as an Asymptotic Form of the Relativistic Equations - p. 171 23. Chapter 6: The Solution of Some Physical Problems on the Basis of the Nonlocal Relativistic Equations Without Taking Into Account the External Forces - p. 178 24. Abstract - p. 179 25. 6.1 The Propagation of Plane Harmonic Waves of Small Amplitude in the Ultra-Relativistic Medium - p. 179 26. 6.2 Shock Waves in Relativistic Gas - p. 205 27. 6.3 The Collision of Nucleons - p. 221 28. Chapter 7: Nonlocal Relativistic Kinetic Equation and Hydrodynamic Enskog Equations Taking Into Account the External Forces - p. 242 29. Abstract - p. 243 30. 7.1 Nonlocal Relativistic Kinetic Equation Taking Into Account the External Forces - p. 243 31. 7.2 The Derivation of the Continuity Equation - p. 245 32. 7.3 The Derivation of the Motion Equation - p. 249 33. 7.4 The Derivation of the Energy Equation - p. 253 34. 7.5 Generalized System of Relativistic Hydrodynamic Enskog Equations - p. 257 35. 7.6 Generalized System of Relativistic Hydrodynamic Enskog Equations for Multicomponent Mixture - p. 264 36. Chapter 8: Generalized Relativistic Euler Equations Taking Into Account External Forces - p. 270 37. Chapter 9: Application of the Generalized Relativistic Kinetic and Hydrodynamic Equations to the Study of Graphene - p. 283 38. Abstract - p. 285 39. 9.1 Features of the Band Structure of Graphene - p. 285 40. 9.2 Generalized Kinetic and Hydrodynamic Equations for Graphene in an Electric Field - p. 293 41. 9.3 Wave Transfer in Graphene - p. 306 42. 9.4 The Hall Effect in the Relativistic Nonlocal Theory of Massless Particles - p. 321 43. Chapter 10: Application of Relativistic Nonlocal Physics in the Theory of Gravitational Field Interaction With a Laser Beam - p. 352 44. Abstract - p. 353 45. 10.1 Nonlocal Physics and Gravitational Waves - p. 353 46. 10.2 Basic Equations of Relativistic Nonlocal Physics Having Regard to External Forces - p. 354 47. 10.3 Calculation of the Tensor Moments for the Laser Beam Evolution - p. 356 48. 10.4 Nonlocal Relativistic Equations in the Explicit Form - p. 363 49. 10.5 Wave Solutions for GFR-Interaction - p. 377 50. Chapter 11: Application of the Generalized Relativistic Hydrodynamic Equations to the Study of the Interaction of Planck Radiation With the Gravitational Field - p. 390 51. Chapter 12: Connection Between Time Quantization in the Frame of Nonlocal Relativistic Physics and Shannon-Nyquist-Kotelnikov Theorem - p. 410 52. Appendices - p. 429 53. Index - p. 451
