MathematicalPrinciples of Theoretical Physics-理论物理的数学原理 目录

noindentbfchapter
1quadgeneralintroductiondotfill
1.1quadchallengesofphysicsandguidingprincipledotfill
1.2quadlawofgravity，darkmatteranddarkenergydotfill
1.3quadfirstprinciplesoffourfundamental interactionsdotfill
1.4quadsymmetryandsymmetry-breakingdotfill
1.5quadunifiedfieldtheorybasedonpidand pridotfill
1.6quadtheoryofstronginteractionsdotfill
1.7quadtheoryofweakinteractionsdotfill
1.8quadnewtheoryofblackholesdotfill
1.9quadtheuniversedotfill
1.10quadsupernovaeexplosionandagn jetsdotfill
1.11quadmulti-particlesystemsand unificationdotfill
1.12quadweaktonmodelofelementary particlesdotfill
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2quadfundamentalprinciplesof physicsdotfill
2.1quadessenceofphysicsdotfill
2.1.1quadgeneralguiding principlesdotfill
2.1.2quadphenomenological methodsdotfill
2.1.3quadfundamentalprinciples inphysicsdotfill
2.1.4quadsymmetrydotfill
2.1.5quadinvarianceand tensorsdotfill
2.1.6quadgeometricinteraction mechanismdotfill
2.1.7quadprincipleof symmetry-breakingdotfill
2.2quadlorentzinvariancedotfill
2.2.1quadlorentz transformationdotfill
2.2.2quadminkowskispaceand lorentztensorsdotfill
2.2.3quadrelativistic invariantsdotfill
2.2.4quadrelativistic mechanicsdotfill
2.2.5quadlorentzinvarianceof electromagnetismdotfill
2.2.6quadrelativisticquantum mechanicsdotfill
2.2.7quaddiracspinorsdotfill
2.3quadeinstein'stheoryofgeneral relativitydotfill
2.3.1quadprincipleofgeneral relativitydotfill
2.3.2quadprincipleof equivalencedotfill
2.3.3quadgeneraltensorsand covariantderivativesdotfill
2.3.4quadeinstein-hilbert actiondotfill
2.3.5quadeinsteingravitational fieldequationsdotfill
2.4quadgaugeinvariancedotfill
2.4.1quad$u(1)$gaugeinvariance ofelectromagnetismdotfill
2.4.2quadgenerator representationsof$su(n)$dotfill
2.4.3quadyang-millsactionof $su(n)$gaugefieldsdotfill
2.4.4quadprincipleofgauge invariancedotfill
2.5quadprincipleoflagrangiandynamics (pld)dotfill
2.5.1quadintroductiondotfill
2.5.2quadelasticwavesdotfill
2.5.3quadclassical electrodynamicsdotfill
2.5.4quadlagrangianactionsin quantummechanicsdotfill
2.5.5quadsymmetriesand conservationlawsdotfill
2.6quadprincipleofhamiltoniandynamics (phd)dotfill
2.6.1quadhamiltoniansystemsin classicalmechanicsdotfill
2.6.2quaddynamicsofconservative systemsdotfill
2.6.3quadphdformaxwell electromagneticfieldsdotfill
2.6.4quadquantumhamiltonian systemsdotfill
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3quadmathematicalfoundationsdotfill
3.1quadbasicconceptsdotfill
3.1.1quadriemannian manifoldsdotfill
3.1.2quadphysicalfieldsand vectorbundlesdotfill
3.1.3quadlineartransformations onvectorbundlesdotfill
3.1.4quadconnectionsand covariantderivativesdotfill
3.2quadanalysisonriemannian manifoldsdotfill
3.2.1quadsobolevspacesoftensor fieldsdotfill
3.2.2quadsobolevembedding theoremdotfill
3.2.3quaddifferential operatorsdotfill
3.2.4quadgaussformuladotfill
3.2.5quadpartialdifferential equationsonriemannianmanifoldsdotfill
3.3quadorthogonaldecompositionfortensor fieldsdotfill
3.3.1quadintroductiondotfill
3.3.2quadorthogonaldecomposition theoremsdotfill
3.3.3quaduniquenessoforthogonal decompositionsdotfill
3.3.4quadorthogonaldecomposition onmanifoldswithboundarydotfill
3.4quadvariationswithdiv$_a$-free constraintsdotfill
3.4.1quadclassicalvariational principledotfill
3.4.2quadderivativeoperatorsof theyang-millsfunctionalsdotfill
3.4.3quadderivativeoperatorof theeinstein-hilbertfunctionaldotfill
3.4.4quadvariationalprinciple withdiv$_a$-freeconstraintdotfill
3.4.5quadscalarpotential theoremdotfill
3.5quad$su(n)$representation invariancedotfill
3.5.1quad$su(n)$gauge representationdotfill
3.5.2quadmanifoldstructureof $su(n)$dotfill
3.5.3quad$su(n)$tensorsdotfill
3.5.4quadintrinsicriemannian metricon$su(n)$dotfill
3.5.5quadrepresentation invarianceofgaugetheorydotfill
3.6quadspectraltheoryofdifferential operatorsdotfill
3.6.1quadphysical backgrounddotfill
3.6.2quadclassicalspectral theorydotfill
3.6.3quadnegativeeigenvaluesof ellipticoperatorsdotfill
3.6.4quadestimatesfornumberof negativeeigenvaluesdotfill
3.6.5quadspectrumofweyl operatorsdotfill
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4quadunifiedfieldtheoryoffourfundamentalnoindentbfqquadqquadquad~interactionsdotfill
4.1quadprinciplesofunifiedfield theorydotfill
4.1.1quadfourinteractionsand
theirinteractionmechanismdotfill
4.1.2quadgeneralintroductionto
unifiedfieldtheorydotfill
4.1.3quadgeometryofunified fieldsdotfill
4.1.4quadgauge symmetry-breakingdotfill
4.1.5quadpidandpridotfill
4.2quadphysicalsupportstopiddotfill
4.2.1quaddarkmatteranddark energydotfill
4.2.2quadnonwell-posednessof einsteinfieldequationsdotfill
4.2.3quadhig