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Mathematical Principles of Theoretical Physics
  • 书号:9787030452894
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作者简介

目录

  • Contents
    \noindent\bfChapter1\quadGeneralIntroduction\dotfill 1
    1.1\quadChallengesofPhysicsandGuidingPrinciple\dotfill 1
    1.2\quadLawofGravity,DarkMatterandDarkEnergy\dotfill 3
    1.3\quadFirstPrinciplesofFourFundamental Interactions\dotfill6
    1.4\quadSymmetryandSymmetry-Breaking\dotfill 13
    1.5\quadUnifiedFieldTheoryBasedonPIDand PRI\dotfill14
    1.6\quadTheoryofStrongInteractions\dotfill 17
    1.7\quadTheoryofWeakInteractions\dotfill 20
    1.8\quadNewTheoryofBlackHoles\dotfill 21
    1.9\quadTheUniverse\dotfill 23
    1.10\quadSupernovaeExplosionandAGN Jets\dotfill27
    1.11\quadMulti-ParticleSystemsand Unification\dotfill28
    1.12\quadWeaktonModelofElementary Particles\dotfill31
    \noindent\bfChapter2\quadFundamentalPrinciplesof Physics\dotfill35
    2.1\quadEssenceofPhysics\dotfill 36
    2.1.1\quadGeneralguiding principles\dotfill36
    2.1.2\quadPhenomenological methods\dotfill37
    2.1.3\quadFundamentalprinciples inphysics\dotfill38
    2.1.4\quadSymmetry\dotfill 41
    2.1.5\quadInvarianceand tensors\dotfill42
    2.1.6\quadGeometricinteraction mechanism\dotfill45
    2.1.7\quadPrincipleof symmetry-breaking\dotfill47
    2.2\quadLorentzInvariance\dotfill 49
    2.2.1\quadLorentz transformation\dotfill49
    2.2.2\quadMinkowskispaceand Lorentztensors\dotfill51
    2.2.3\quadRelativistic invariants\dotfill55
    2.2.4\quadRelativistic mechanics\dotfill56
    2.2.5\quadLorentzinvarianceof electromagnetism\dotfill58
    2.2.6\quadRelativisticquantum mechanics\dotfill60
    2.2.7\quadDiracspinors\dotfill 62
    2.3\quadEinstein'sTheoryofGeneral Relativity\dotfill64
    2.3.1\quadPrincipleofgeneral relativity\dotfill64
    2.3.2\quadPrincipleof equivalence\dotfill66
    2.3.3\quadGeneraltensorsand covariantderivatives\dotfill67
    2.3.4\quadEinstein-Hilbert action\dotfill71
    2.3.5\quadEinsteingravitational fieldequations\dotfill73
    2.4\quadGaugeInvariance\dotfill 74
    2.4.1\quad$U(1)$gaugeinvariance ofelectromagnetism\dotfill74
    2.4.2\quadGenerator representationsof$SU(N)$\dotfill77
    2.4.3\quadYang-Millsactionof $SU(N)$gaugefields\dotfill79
    2.4.4\quadPrincipleofgauge invariance\dotfill83
    2.5\quadPrincipleofLagrangianDynamics (PLD)\dotfill84
    2.5.1\quadIntroduction\dotfill 84
    2.5.2\quadElasticwaves\dotfill 86
    2.5.3\quadClassical electrodynamics\dotfill86
    2.5.4\quadLagrangianactionsin quantummechanics\dotfill91
    2.5.5\quadSymmetriesand conservationlaws\dotfill94
    2.6\quadPrincipleofHamiltonianDynamics (PHD)\dotfill98
    2.6.1\quadHamiltoniansystemsin classicalmechanics\dotfill98
    2.6.2\quadDynamicsofconservative systems\dotfill102
    2.6.3\quadPHDforMaxwell electromagneticfields\dotfill105
    2.6.4\quadQuantumHamiltonian systems\dotfill107
    \noindent\bfChapter3\quadMathematicalFoundations\dotfill111
    3.1\quadBasicConcepts\dotfill 113
    3.1.1\quadRiemannian manifolds\dotfill113
    3.1.2\quadPhysicalfieldsand vectorbundles\dotfill117
    3.1.3\quadLineartransformations onvectorbundles\dotfill121
    3.1.4\quadConnectionsand covariantderivatives\dotfill124
    3.2\quadAnalysisonRiemannian Manifolds\dotfill127
    3.2.1\quadSobolevspacesoftensor fields\dotfill127
    3.2.2\quadSobolevembedding theorem\dotfill131
    3.2.3\quadDifferential operators\dotfill133
    3.2.4\quadGaussformula\dotfill 137
    3.2.5\quadPartialdifferential equationsonRiemannianmanifolds\dotfill138
    3.3\quadOrthogonalDecompositionforTensor Fields\dotfill140
    3.3.1\quadIntroduction\dotfill 140
    3.3.2\quadOrthogonaldecomposition theorems\dotfill142
    3.3.3\quadUniquenessoforthogonal decompositions\dotfill145
    3.3.4\quadOrthogonaldecomposition onmanifoldswithboundary\dotfill149
    3.4\quadVariationswithdiv$_A$-Free Constraints\dotfill150
    3.4.1\quadClassicalvariational principle\dotfill150
    3.4.2\quadDerivativeoperatorsof theYang-Millsfunctionals\dotfill152
    3.4.3\quadDerivativeoperatorof theEinstein-Hilbertfunctional\dotfill153
    3.4.4\quadVariationalprinciple withdiv$_A$-freeconstraint\dotfill156
    3.4.5\quadScalarpotential theorem\dotfill160
    3.5\quad$SU(N)$Representation Invariance\dotfill162
    3.5.1\quad$SU(N)$gauge representation\dotfill162
    3.5.2\quadManifoldstructureof $SU(N)$\dotfill164
    3.5.3\quad$SU(N)$tensors\dotfill 167
    3.5.4\quadIntrinsicRiemannian metricon$SU(N)$\dotfill169
    3.5.5\quadRepresentation invarianceofgaugetheory\dotfill172
    3.6\quadSpectralTheoryofDifferential Operators\dotfill173
    3.6.1\quadPhysical background\dotfill173
    3.6.2\quadClassicalspectral theory\dotfill174
    3.6.3\quadNegativeeigenvaluesof ellipticoperators\dotfill176
    3.6.4\quadEstimatesfornumberof negativeeigenvalues\dotfill178
    3.6.5\quadSpectrumofWeyl operators\dotfill182
    \noindent\bfChapter4\quadUnifiedFieldTheoryofFourFundamental\noindent\bf\qquad\qquad\quad~Interactions\dotfill 186
    4.1\quadPrinciplesofUnifiedField Theory\dotfill187
    4.1.1\quadFourinteractionsand
    theirinteractionmechanism\dotfill187
    4.1.2\quadGeneralintroductionto
    unifiedfieldtheory\dotfill190
    4.1.3\quadGeometryofunified fields\dotfill193
    4.1.4\quadGauge symmetry-breaking\dotfill196
    4.1.5\quadPIDandPRI\dotfill 197
    4.2\quadPhysicalSupportstoPID\dotfill 200
    4.2.1\quadDarkmatteranddark energy\dotfill200
    4.2.2\quadNonwell-posednessof Einsteinfieldequations\dotfill202
    4.2.3\quadHiggsmechanismandmass generation\dotfill204
    4.2.4\quadGinzburg-Landau superconductivity\dotfill208
    4.3\quadUnifiedFieldModelBasedonPIDand PRI\dotfill209
    4.3.1\quadUnifiedfieldequations basedonPID\dotfill209
    4.3.2\quadCouplingparametersand physicaldimensions\dotfill213
    4.3.3\quadStandardformofunified fieldequations\dotfill214
    4.3.4\quadPotentialsoftheweak andstrongforces\dotfill216
    4.3.5\quadGauge-fixing problem\dotfill217
    4.4\quadDualityandDecouplingofInteraction Fields\dotfill219
    4.4.1\quadDuality\dotfill 219
    4.4.2\quadGravitationalfield equationsderivedbyPID\dotfill221
    4.4.3\quadModifiedQED model\dotfill222
    4.4.4\quadStronginteractionfield equations\dotfill225
    4.4.5\quadWeakinteractionfield equations\dotfill227
    4.5\quadStrongInteractionPotentials\dotfill 228
    4.5.1\quadStronginteraction potentialofelementaryparticles\dotfill228
    4.5.2\quadLayeredformulasof stronginteractionpotentials\dotfill233
    4.5.3\quadQuark confinement\dotfill235
    4.5.4\quadAsymptotic freedom\dotfill237
    4.5.5\quadModifiedYukawa potential\dotfill239
    4.5.6\quadPhysicalconclusionsfor nucleonforce\dotfill242
    4.5.7\quadShort-rangenatureof stronginteraction\dotfill243
    4.6\quadWeakInteractionTheory\dotfill 244
    4.6.1\quadDualequationsofweak interactionpotentials\dotfill244
    4.6.2\quadLayeredformulasofweak forces\dotfill247
    4.6.3\quadPhysicalconclusionsfor weakforces\dotfill250
    4.6.4\quadPIDmechanismof spontaneoussymmetrybreaking\dotfill251
    4.6.5\quadIntroductiontothe classicalelectroweaktheory\dotfill255
    4.6.6\quadProblemsinWS theory\dotfill260
    \noindent\bfChapter5\quadElementaryParticles\dotfill 263
    5.1\quadBasicKnowledgeofParticle Physics\dotfill264
    5.1.1\quadClassificationof particles\dotfill264
    5.1.2\quadQuantumnumbers\dotfill 266
    5.1.3\quadParticle transitions\dotfill271
    5.1.4\quadConservation laws\dotfill274
    5.1.5\quadBasicdataof particles\dotfill276
    5.2\quadQuarkModel\dotfill 277
    5.2.1\quadEightfoldway\dotfill 277
    5.2.2\quadIrreducible representationsof$SU(N)$\dotfill281
    5.2.3\quadPhysicalexplanationof irreduciblerepresentations\dotfill285
    5.2.4\quadComputationsfor irreduciblerepresentations\dotfill289
    5.2.5\quadSakatamodelof hadrons\dotfill294
    5.2.6\quadGell-Mann-Zweig'squark model\dotfill295
    5.3\quadWeaktonModelofElementary Particles\dotfill298
    5.3.1\quadDecaymeanstheinterior structure\dotfill298
    5.3.2\quadTheoreticalfoundations fortheweaktonmodel\dotfill299
    5.3.3\quadWeaktonsandtheir quantumnumbers\dotfill304
    5.3.4\quadWeaktonconstituentsand dualityofmediators\dotfill305
    5.3.5\quadWeaktonconfinementandmassgeneration\dotfill307
    5.3.6\quadQuantumrulesfor weaktons\dotfill309
    5.4\quadMechanismsofSubatomicDecaysand ElectronRadiations\dotfill312
    5.4.1\quadWeakton exchanges\dotfill312
    5.4.2\quadConservation laws\dotfill314
    5.4.3\quadDecaytypes\dotfill 316
    5.4.4\quadDecaysand scatterings\dotfill317
    5.4.5\quadElectron structure\dotfill322
    5.4.6\quadMechanismof bremsstrahlung\dotfill323
    5.5\quadStructureofMediatorCloudsAround SubatomicParticles\dotfill324
    5.5.1\quadColorquantum number\dotfill324
    5.5.2\quadGluons\dotfill 326
    5.5.3\quadColoralgebra\dotfill 329
    5.5.4\quad$w^*$-color algebra\dotfill334
    5.5.5\quadMediatorcloudsof subatomicparticles\dotfill 338
    \noindent\bfChapter6\quadQuantumPhysics\dotfill 342
    6.1\quadIntroduction\dotfill342
    6.2\quadFoundationsofQuantumPhysics\dotfill345
    6.2.1\quadBasic postulates\dotfill345
    6.2.2\quadQuantumdynamic equations\dotfill348
    6.2.3\quadHeisenberguncertainty relationandPauliexclusionprinciple\dotfill 354
    6.2.4\quadAngularmomentum rule\dotfill357
    6.3\quadSolarNeutrinoProblem\dotfill 361
    6.3.1\quadDiscrepancyofthesolar neutrinos\dotfill361
    6.3.2\quadNeutrino oscillations\dotfill365
    6.3.3\quadMixingmatrixand neutrinomasses\dotfill367
    6.3.4\quadMSWeffect\dotfill 369
    6.3.5\quadMasslessneutrino oscillationmodel\dotfill370
    6.3.6\quadNeutrinonon-oscillation mechanism\dotfill373
    6.4\quadEnergyLevelsofSubatomic Particles\dotfill374
    6.4.1\quadPreliminaries\dotfill 374
    6.4.2\quadSpectralequationsof boundstates\dotfill377
    6.4.3\quadChargedleptonsand quarks\dotfill383
    6.4.4\quadBaryonsand mesons\dotfill386
    6.4.5\quadEnergyspectrumof mediators\dotfill388
    6.4.6\quadDiscretenessofenergy spectrum\dotfill389
    6.5\quadFieldTheoryofMulti-Particle Systems\dotfill394
    6.5.1\quadIntroduction\dotfill 394
    6.5.2\quadBasicpostulatesfor \itN-bodyquantumphysics\dotfill395
    6.5.3\quadFieldequationsof multi-particlesystems\dotfill398
    6.5.4\quadUnifiedfieldmodel couplingmatterfields\dotfill403
    6.5.5\quadAtomicspectrum\dotfill 407
    \noindent\bfChapter7\quadAstrophysicsandCosmology\dotfill 411
    7.1\quadAstrophysicalFluidDynamics\dotfill 412
    7.1.1\quadFluiddynamicequations onRiemannianmanifolds\dotfill412
    7.1.2\quadSchwarzschildand Tolman-Oppenheimer-Volkoff(TOV)metrics\dotfill 413
    7.1.3\quadDifferentialoperators insphericalcoordinates\dotfill419
    7.1.4\quadMomentum representation\dotfill422
    7.1.5\quadAstrophysicalFluid DynamicsEquations\dotfill425
    7.2\quadStars\dotfill429
    7.2.1\quadBasicknowledge\dotfill 429
    7.2.2\quadMaindrivingforcefor stellardynamics\dotfill431
    7.2.3\quadStellarinterior circulation\dotfill435
    7.2.4\quadStellaratmospheric circulations\dotfill440
    7.2.5\quadDynamicsofstarswith variableradii\dotfill443
    7.2.6\quadMechanismofsupernova explosion\dotfill448
    7.3\quadBlackHoles\dotfill 450
    7.3.1\quadGeometricrealizationof blackholes\dotfill450
    7.3.2\quadBlackhole theorem\dotfill453
    7.3.3\quadCritical $\delta$-factor\dotfill455
    7.3.4\quadOriginofstarsand galaxies\dotfill458
    7.4\quadGalaxies\dotfill 461
    7.4.1\quadIntroduction\dotfill 461
    7.4.2\quadGalaxydynamics\dotfill 464
    7.4.3\quadSpiralgalaxies\dotfill 467
    7.4.4\quadActivegalacticnuclei (AGN)andjets\dotfill470
    7.5\quadTheUniverse\dotfill 475
    7.5.1\quadClassicaltheoryofthe Universe\dotfill475
    7.5.2\quadGlobularuniversewith boundary\dotfill481
    7.5.3\quadSphericalUniverse withoutboundary\dotfill485
    7.5.4\quadNewcosmology\dotfill 489
    7.6\quadTheoryofDarkMatterandDark Energy\dotfill492
    7.6.1\quadDarkenergyanddark matterphenomena\dotfill492
    7.6.2\quadPIDcosmologicalmodel anddarkenergy\dotfill493
    7.6.3\quadPIDgravitational interactionformula\dotfill497
    7.6.4\quadAsymptoticrepulsionof gravity\dotfill499
    7.6.5\quadSimplifiedgravitational formula\dotfill504
    7.6.6\quadNatureofdarkmatter anddarkenergy\dotfill506
    \noindent\bfBibliography\dotfill511
    \noindent\bfIndex\dotfill515
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