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Tables of Contents for Classical Relativistic Many-Body Dynamics
Chapter/Section Title
Page #
Page Count
Preface and Acknowledgments
xiii
Introduction
1
30
The Relativistic Particle System
1
3
Particle Electrodynamics
4
8
The Off-Shell Momentum
12
3
The Covariant Potential
15
3
The Hamiltonian Theory
18
2
Comparison to Field Theory
20
4
Exotic World Lines
24
3
Outline of the Work
27
4
Frame-Dependent Kinematics
31
22
Global Inertial Observers
32
2
Frame Observables
34
3
Time-Derivative Vectors
34
1
Scalar and Vector Products
35
2
World Lines
37
3
Time-Evolution Transformations
40
1
Local Observables
41
1
Background Transformations
42
6
Graphical Representation
43
3
Alternate Graphical Representation
46
1
Equation Representation
47
1
Transformations of the Frame Observables
48
2
Co-Moving Frames
50
2
The No Interaction Theorem
52
1
Covariant Kinematics
53
28
Covariant Vectors
53
2
Invariant Scalar Products
55
4
Regular Parametric Representations
59
6
Comparison to the Euclidean Time Parameter
62
1
Parameter vs. Background Transformations
62
1
Natural vs. Staggered Parameters
63
2
The Derivatives of the Position Vector
65
7
Derivatives with Respect to Arc Length
66
4
Derivatives with Respect to Arbitrary Parameter
70
2
The Co-Moving Basis
72
6
The Orthonormal Tetrad
74
3
Arbitrary Parameter Representations
77
1
Correlated Representations
78
3
The Dynamical Theory
81
40
The Dynamical Evolution Time
81
18
The Frame-Time Method
82
4
The World Time Method
86
2
The Free Particle Limit
88
1
The Local Invariant Dilation
89
2
The Event State
91
5
The Two-Body Separation Vector
96
1
Invariance vs. Constancy
96
2
Interpretation of the World Time
98
1
The Dynamical Law
99
10
The Generalized Coordinates and Velocities
99
1
The Two-Body Reduced Motion
100
3
The Covariant Momentum
103
2
The Invariant Potential
105
2
The Invariant Kinetic Energy
107
1
The Covariant Hamilton's Equations
108
1
Configuration Space vs. Phase Space
108
1
The Covariant Center of Mass
109
3
The Synchronization Postulate
112
7
Summary of Dynamical Postulates
119
2
The Lagrangian-Hamiltonian Theory
121
66
The Euler-Lagrange Equations
122
2
The Canonical Momentum
124
2
The Hamilton's Equations
126
1
The Two-Body System
126
54
The Euler-Lagrange Equations
130
1
The Canonical Momenta
131
2
The Covariant Angular Momentum Tensor
133
4
The Hyperbolic Angle Coordinates
137
9
The Integrals of the Motion
146
4
The Orbit Equations
150
4
Projections onto the Coordinate Planes
154
1
Bound and Unbound Orbits
155
3
Proof that Bound Orbits are Closed
158
1
The Time Dependence of the Solutions
159
1
The Hamilton's Equations
160
1
The Hamilton-Jacobi Equation
161
3
The Action Variables
164
4
The Center-of-Mass Temporal Speed
168
1
The World Line Solutions
169
5
Solutions in the Piron-Reuse Frame
174
5
The One-Body Limit
179
1
Comparison to Frame-Dependent Theory
180
2
Dynamical Applications
182
5
The Harmonic Oscillator
182
1
The Duffing Oscillator
183
2
Statistical Mechanics
185
2
The Coulomb Potential (I)
187
38
The 1 + 1-Dimensional Orbit Equation
191
3
The Invariant Eccentricity
194
2
The Orbits of the Reduced Motion
196
4
The Type I Solution
197
1
The Type II Solution
198
2
The Time Dependence of the Reduced Motion
200
3
The Reduced Trajectories in Time
203
3
The Frame Speeds of the Two Particles
206
9
Solutions for which ρ → 0
212
2
Solutions for which ρ → ∞
214
1
The Center-of-Mass Motion for Scattering
215
2
The Particle Masses
217
3
The Scattering System in the Mass Limits
220
4
The Equal Mass Limit
221
1
The One-Body Limit
222
2
The Stuckelberg Pair Annihilation Model
224
1
The Coulomb Potential (II)
225
42
The 2+1-Dimensional Orbit Equation
227
4
The Invariant Eccentricity
231
2
The Orbits in the Meridional Plane
233
7
The Type I Solution
234
2
The Type II Solution
236
4
The Full Reduced Orbits
240
9
The Type I Solution
240
4
The Type II Solution
244
5
The Time Dependence of the Reduced Motion
249
9
The Type I Solution
250
3
The Period of Bound Orbits
253
2
The Type II Solution
255
3
The Piron-Reuse Solutions
258
1
The Semi-Classical Quantization
259
4
The Particle World Lines
263
1
The Significance of the Work of Cook
264
1
Summary of the Coulomb Potential
264
3
Conclusions and Suggestions
267
12
Summary of the Investigation
267
2
Possible Classical Experiments
269
8
The Gravitational System
270
4
The Electromagnetic System
274
2
Recently Suggested Experimental Tests
276
1
Final Comments to the Reader
277
2
A The Geometry of World Lines
279
48
The Geometry of 1-d Curves
279
8
Curves in the Space En
279
2
Curves in the Space E3
281
2
Applications to Nonrelativistic Motion
283
2
Applications to Relativistic Motion
285
2
Spacetime Curves
287
23
Special Relativistic Kinematics
287
6
World Lines as Regular Curves
293
4
The Unit Binormal Four-Vector
297
9
The Unit Trinormal and Orthonormal Tetrad
306
4
The Covariant Serret-Frenet Equations
310
9
The Active Lorentz Transformation
319
6
The Fermi-Walker Operator
320
1
The General Co-Moving Frame
321
4
Conclusions
325
2
B The Solutions Derived by Cook
327
6
C The No Interaction Theorem
333
10
Comments on the Proof
340
3
D Classical Pair Annihilation
343
8
Bibliography
351
6
Index
357