MathematicalPrinciples of Theoretical Physics-理论物理的数学原理 目录
noindent\bfchapter
1\quadgeneralintroduction\dotfill
1.1\quadchallengesofphysicsandguidingprinciple\dotfill
1.2\quadlawofgravity，darkmatteranddarkenergy\dotfill
1.3\quadfirstprinciplesoffourfundamental interactions\dotfill
1.4\quadsymmetryandsymmetry-breaking\dotfill
1.5\quadunifiedfieldtheorybasedonpidand pri\dotfill
1.6\quadtheoryofstronginteractions\dotfill
1.7\quadtheoryofweakinteractions\dotfill
1.8\quadnewtheoryofblackholes\dotfill
1.9\quadtheuniverse\dotfill
1.10\quadsupernovaeexplosionandagn jets\dotfill
1.11\quadmulti-particlesystemsand unification\dotfill
1.12\quadweaktonmodelofelementary particles\dotfill
\noindent\bfchapter
2\quadfundamentalprinciplesof physics\dotfill
2.1\quadessenceofphysics\dotfill
2.1.1\quadgeneralguiding principles\dotfill
2.1.2\quadphenomenological methods\dotfill
2.1.3\quadfundamentalprinciples inphysics\dotfill
2.1.4\quadsymmetry\dotfill
2.1.5\quadinvarianceand tensors\dotfill
2.1.6\quadgeometricinteraction mechanism\dotfill
2.1.7\quadprincipleof symmetry-breaking\dotfill
2.2\quadlorentzinvariance\dotfill
2.2.1\quadlorentz transformation\dotfill
2.2.2\quadminkowskispaceand lorentztensors\dotfill
2.2.3\quadrelativistic invariants\dotfill
2.2.4\quadrelativistic mechanics\dotfill
2.2.5\quadlorentzinvarianceof electromagnetism\dotfill
2.2.6\quadrelativisticquantum mechanics\dotfill
2.2.7\quaddiracspinors\dotfill
2.3\quadeinstein'stheoryofgeneral relativity\dotfill
2.3.1\quadprincipleofgeneral relativity\dotfill
2.3.2\quadprincipleof equivalence\dotfill
2.3.3\quadgeneraltensorsand covariantderivatives\dotfill
2.3.4\quadeinstein-hilbert action\dotfill
2.3.5\quadeinsteingravitational fieldequations\dotfill
2.4\quadgaugeinvariance\dotfill
2.4.1\quad$u(1)$gaugeinvariance ofelectromagnetism\dotfill
2.4.2\quadgenerator representationsof$su(n)$\dotfill
2.4.3\quadyang-millsactionof $su(n)$gaugefields\dotfill
2.4.4\quadprincipleofgauge invariance\dotfill
2.5\quadprincipleoflagrangiandynamics (pld)\dotfill
2.5.1\quadintroduction\dotfill
2.5.2\quadelasticwaves\dotfill
2.5.3\quadclassical electrodynamics\dotfill
2.5.4\quadlagrangianactionsin quantummechanics\dotfill
2.5.5\quadsymmetriesand conservationlaws\dotfill
2.6\quadprincipleofhamiltoniandynamics (phd)\dotfill
2.6.1\quadhamiltoniansystemsin classicalmechanics\dotfill
2.6.2\quaddynamicsofconservative systems\dotfill
2.6.3\quadphdformaxwell electromagneticfields\dotfill
2.6.4\quadquantumhamiltonian systems\dotfill
\noindent\bfchapter
3\quadmathematicalfoundations\dotfill
3.1\quadbasicconcepts\dotfill
3.1.1\quadriemannian manifolds\dotfill
3.1.2\quadphysicalfieldsand vectorbundles\dotfill
3.1.3\quadlineartransformations onvectorbundles\dotfill
3.1.4\quadconnectionsand covariantderivatives\dotfill
3.2\quadanalysisonriemannian manifolds\dotfill
3.2.1\quadsobolevspacesoftensor fields\dotfill
3.2.2\quadsobolevembedding theorem\dotfill
3.2.3\quaddifferential operators\dotfill
3.2.4\quadgaussformula\dotfill
3.2.5\quadpartialdifferential equationsonriemannianmanifolds\dotfill
3.3\quadorthogonaldecompositionfortensor fields\dotfill
3.3.1\quadintroduction\dotfill
3.3.2\quadorthogonaldecomposition theorems\dotfill
3.3.3\quaduniquenessoforthogonal decompositions\dotfill
3.3.4\quadorthogonaldecomposition onmanifoldswithboundary\dotfill
3.4\quadvariationswithdiv$_a$-free constraints\dotfill
3.4.1\quadclassicalvariational principle\dotfill
3.4.2\quadderivativeoperatorsof theyang-millsfunctionals\dotfill
3.4.3\quadderivativeoperatorof theeinstein-hilbertfunctional\dotfill
3.4.4\quadvariationalprinciple withdiv$_a$-freeconstraint\dotfill
3.4.5\quadscalarpotential theorem\dotfill
3.5\quad$su(n)$representation invariance\dotfill
3.5.1\quad$su(n)$gauge representation\dotfill
3.5.2\quadmanifoldstructureof $su(n)$\dotfill
3.5.3\quad$su(n)$tensors\dotfill
3.5.4\quadintrinsicriemannian metricon$su(n)$\dotfill
3.5.5\quadrepresentation invarianceofgaugetheory\dotfill
3.6\quadspectraltheoryofdifferential operators\dotfill
3.6.1\quadphysical background\dotfill
3.6.2\quadclassicalspectral theory\dotfill
3.6.3\quadnegativeeigenvaluesof ellipticoperators\dotfill
3.6.4\quadestimatesfornumberof negativeeigenvalues\dotfill
3.6.5\quadspectrumofweyl operators\dotfill
\noindent\bfchapter
4\quadunifiedfieldtheoryoffourfundamental\noindent\bf\qquad\qquad\quad~interactions\dotfill
4.1\quadprinciplesofunifiedfield theory\dotfill
4.1.1\quadfourinteractionsand
theirinteractionmechanism\dotfill
4.1.2\quadgeneralintroductionto
unifiedfieldtheory\dotfill
4.1.3\quadgeometryofunified fields\dotfill
4.1.4\quadgauge symmetry-breaking\dotfill
4.1.5\quadpidandpri\dotfill
4.2\quadphysicalsupportstopid\dotfill
4.2.1\quaddarkmatteranddark energy\dotfill
4.2.2\quadnonwell-posednessof einsteinfieldequations\dotfill
4.2.3\quadhig
