理论物理的数学原理

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\quadHig