Deformed Spacetime: Geometrizing Interactions in Four and Five Dimensions

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Springer Science & Business Media, 4 set 2007 - 506 pagine

This volume provides a detailed discussion of the mathematical aspects and physical applications of a new geometrical structure of space-time, based on a generalization ("deformation") of the usual Minkowski space, as supposed to be endowed with a metric whose coefficients depend on the energy. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism.

 

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Sommario

193 Phenomenological 5D Metrics of Fundamental Interactions
285
Einsteins Field Equations in 5 and Their Solutions
287
202 Vacuum Einsteins Equations
290
Power Ansatz
291
2023 Phenomenological Metrics in the Power Ansatz
292
203 Solving Einsteins Equations
296
204 Discussion of Solutions
298
205 DR5 and Warped Geometry
300

332 Boost in a Generic Direction
27
333 Symmetrization of Deformed Boosts
31
334 Choosing the Boost Direction in DSR
33
336 Velocity Composition Law in M and the Invariant Maximal Speed
34
337 DSR and Lorentzian Relativity
38
34 Kinematics and Wave Propagation in a Deformed Minkowski Space
40
342 Deformed Relativistic Kinematics
43
343 Wave Propagation in a Deformed SpaceTime
47
35 Field Deformation
50
Metric Description of Interactions
53
412 Weak Interaction
55
413 Strong Interaction
56
414 Gravitation
58
42 Threshold Energies and Recursive Metrics
60
43 Asymptotic Metrics
62
44 DSR as Metric Gauge Theory
64
MATHEMATICS OF DEFORMED SPACETIME
66
Generalized Minkowski Spaces and Killing Symmetries
69
52 Maximal Killing Group of a TVDimensional Generalized Minkowski Space
70
522 Killing Equations in a NDimensional Generalized Minkowski Space
71
523 Maximal Killing Group of MN
74
524 Solution of Killing Equations in a 4D Generalized Minkowski Space
76
Infinitesimal Structure of Generalized SpaceTime Rotation Groups
79
612 Dependence of the Transformation Commutativity on the Parametric Level
82
62 The Case of a 4D Generalized Minkowski Space
85
622 Decomposition of the Parametric 4Tensor 𝛿𝜔g
86
63 SpaceTime Rotations in a 4D Deformed Minkowski Space
88
632 Decomposition of the Parametric 4Tensor in DSR
90
633 Infinitesimal Transformations of the 4D Deformed Lorentz Group
92
634 4D Deformed Lorentz Algebra
95
Finite Structure of Deformed Chronotopical Groups
99
712 Deformed Lorentz Group oDSR
100
72 Finite SpaceTime Rotations in M
101
722 Finite Deformed Boost along a Coordinate Axis
106
723 Finite Deformed Rotation about a Coordinate Axis
114
724 Antisymmetric Tensor of Deformed Rotation Parameters
120
725 Parameter Range and Group Compactness
123
726 Deformed Boosts as Pseudorotations
125
73 Deformed True Rotation about a Generic Axis
127
74 Finite 3D Deformed Boosts in a Generic Direction
138
742 Deformed Generic Boost from Velocity Decomposition
142
743 Parametric Change of Basis for a Deformed Boost in a Generic Direction
146
Deformed SpaceTime Translations in Four Dimensions
154
82 The Group of 4D Deformed Translations
159
822 Mixed Deformed Poincaré Algebra
161
823 Infinitesimal and Finite Deformed Translations in DSR
165
Deformed Minkowski Space as Generalized Lagrange Space
171
92 Generalized Lagrangian Structure of M
176
93 Canonical Metric Connection of M
177
Gauge Fields
179
EXPERIMENTS ON DEFORMED SPACETIME
182
Lorentz and CPT Symmetries in DSR
185
Lorentz Invariance Breakdown A Brief Survey
188
112 Experimental Tests
191
Superluminal Propagation of Electromagnetic Waves
195
The Shadow of Light Lorentzian Violation of Electrodynamics in Photon Systems
198
132 Crossing Photon Beam Experiments
204
Hollow Wave LLI Breakdown and Violation of Electrodynamics
206
The Coil Experiment
213
142 LLI Breakdown Parameter
216
143 Interpretation in Terms of DSR
219
The Speed of Gravity
221
152 Cavendishlike Experiment
224
1522 Measurement Analysis and Results
226
153 Interpretation in Terms of DSR
231
Piezonuclear Reactions in Cavitated Water
234
162 Cavitating Water Experiments
237
1622 Second Experiment
238
1623 Third Experiment
240
163 Phenomenological Model of Piezonuclear Reactions
242
1632 Application to Europium
245
1633 Limits of the Classical Model
248
1635 Threshold Energy for Piezonuclear Reactions
249
Piezonuclear Reactions in Cavitated Solutions
253
1712 HadroLeptonic Thorium Decay in DSR
255
172 Evidence for Neutron Emission in NonMinkowskian Conditions
257
1722 Second Investigation
266
DEFORMED SPACETIME IN FIVE DIMENSIONS GEOMETRY
272
Multidimensional SpaceTime
275
Embedding Deformed Minkowski Space in a 5D Riemann Space
279
192 The 5D SpaceTimeEnergy Manifold 𝕽₅
281
Killing Equations in the Space 𝕽₅
302
212 The Hypothesis ϒ of Functional Independence
306
213 Solving Killing Equations in 𝕽₅ in the ϒHypothesis
308
214 Power Ansatz and Reductivity of the Hypothesis ϒ
310
Killing Symmetries for the 5D Metrics of Fundamental Interactions
313
2212 Killing Isometries for Electromagnetic and Weak Metrics
317
2213 Solution of Killing Equations below Threshold with Violated ϒHypothesis
318
222 Strong Interaction
320
2222 Killing Isometries for Strong Metric
323
2223 Solution of Strong Killing Equations above Threshold with Violated ϒHypothesis
326
223 Gravitational Interaction
328
2232 The 5D ϒViolating Metrics of Gravitation
331
224 InfinitesimalAlgebraic Structure of Killing Symmetries in 𝕽₅
335
2241 Metric with Constant SpaceTime Coefficients
336
2242 Strong Metric for Violated ϒHypothesis
342
2243 Power Ansatz Metrics with Violated ϒHypothesis
344
225 Features of Killing Isometries in 𝕽₅
353
DEFORMED SPACETIME IN FIVE DIMENSIONS DYNAMICS
355
Dynamics in DR5
357
231 Proper Time in DR5
358
Solution of the Geodesic Equations in the Power Ansatz
360
242 Geodesic Motions for the 5D Metrics of Fundamental Interactions
364
2422 Generating Function for Strong and Gravitational Metrics
366
2423 Geodesies for Electromagnetic and Weak Interactions
368
2424 Geodesies for Strong and Gravitational Interactions
369
243 Gravitational Metric of the Einstein Type
374
244 Class VIII and the Heisenberg TimeEnergy Uncertainty
375
Complete Solutions of Geodesic Equations
379
251 Minkowskian Behavior
380
252 NonMinkowskian Behavior
381
2522 Strong Interaction above Threshold
383
2523 Gravitational Interaction above Threshold
384
253 Slicing and Dynamics
387
Conclusions and Perspectives
389
Reductivity of the ϒHypothesis
395
A12 Class II
397
A13 Class III
398
A16 Class VI
399
A17 Class VII
400
A110 Class X
401
A111 Class XI
403
A112 Class XII
404
A2 Solution of the 5D Killing Equations for Totally Violated ϒHypothesis
406
A22 Case 2
408
A23 Case 3
409
A24 Case 4
410
Gravitational Killing Symmetries
412
B11 Ia
414
B2 Form II
417
B22 IIb
418
B3 Form III
421
B32 IIIb
422
B4 Form IV
423
B41 IVa
424
B51 Va
425
B6 Form VI
426
B61 VIa
427
B7 Form VII
430
B72 VIIIb
432
B81 VHIa
433
B9 Form IX
435
B92 IXb
436
B10 Form X
437
B11 Form XI
440
B112 Xlb
442
Explicit and Implicit Forms of Geodesies for the 12 Classes of Solutions of Einsteins Equations in Vacuum in the Power Ansatz
445
C2 Class II
446
C3 Class III
448
C4 Class IV
456
C5 Class V
457
C6 Class VI
471
C7 Class VII
472
C8 Class VIII
475
C9 Class IX
476
C10 Class X
477
Cll Class XI
478
C12 Class XII
479
References
481
Index
490
Copyright

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