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| 目錄：
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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$U1$gaugeinvariance ofelectromagnetism\dotfill
2.4.2\quadGenerator representationsof$SUN$\dotfill
2.4.3\quadYang-Millsactionof $SUN$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$SUN$Representation Invariance\dotfill
3.5.1\quad$SUN$gauge representation\dotfill
3.5.2\quadManifoldstructureof $SUN$\dotfill
3.5.3\quad$SUN$tensors\dotfill
3.5.4\quadIntrinsicRiemannian metricon$SUN$\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
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chapter{General Introduction}
section{Challenges of Physics and Guiding Principle} la{s0.1}
{ bf Challenges of theoretical physics}
medskip
Physics is an important part of science of Nature， and is one of
the oldest science disciplines. It intersects with many other
disciplines of science such as mathematics and chemistry.
Great progresses have been made in physics since the second half
of the 19th century. The Maxwell equation， the Einstein special
and general relativity and quantum mechanics have become
cornerstones of modern physics. Nowadays physics faces new
challenges. A partial list of most important and challenging ones
is given as follows.
begin{quote}
{ sf begin{itemize}
item[1.] What is dark matter?
item[2.] What is dark energy?
end{itemize}
end{quote}
Dark matter and dark energy are two great mysteries in physics.
Their gravitational effects are observed and are not accounted for
in the Einstein gravitational field equations， and in the
Newtonian gravitational laws.
begin{quote}
{ sf begin{itemize}
item[3.] Is there a Big-Bang? What is the origin of our
Universe? Is our Universe static? What is the geometric shape of
our Universe?
end{itemize}
end{quote}
These are certainly most fundamental questions about our
Universe. The current dominant thinking is that the Universe was
originated from the Big-Bang. However， there are many unsolved
mysteries associated with the Big-Bang theory， such as the horizon
problem， the cosmic microwave radiation problem， and the flatness
problem.
begin{quote}
{ sf begin{itemize}
item[4.] What is the main characteristic of a black hole?
end{itemize}
end{quote}
Black holes are fascinating objects in our Universe. However，
there are a lot of confusions about black holes， even its very
definition.
begin{quote}
{ sf begin{itemize}
item[5.] Quark Confinement: Why has there never been observed
free quarks?
end{itemize}
end{quote}
There are 12 fundamental subatomic particles， including six
leptons and six quarks. This is a mystery for not being able to
observe free quarks and gluons.
begin{quote}
{ sf begin{itemize}
item[6.] Baryon asymmetry: Where are there more particles than
anti-particles?
end{itemize}
end{quote}
Each particle has its own antiparticle. It is clear that there are
far more particles in this Universe than anti-particles. What is
the reason? This is another mystery， which is also related to the
formation and origin of our Universe.
begin{quote}
{ sf begin{itemize}
item[7.] Are there weak and strong interactionforce formulas?
end{itemize}
end{quote}
We know that the Newton and the Coulomb formulas are basic force
formulas for gravitational force and for electromagnetic force.
One longstanding problem is to derive similar force formulas for
the weak and the strong interactions， which are responsible for
holding subatomic particles together and for various decays.
begin{quote}
{ sf begin{itemize}
item[8.] What is the strong interaction potential of nucleus?
Can we derive the Yukawa potential from first principles?
end{itemize}
end{quote}
begin{quote}
{ sf begin{itemize}
item[9.] Why do leptons not participate in the strong
interaction?
end{itemize}
end{quote}
begin{quote}
{ sf begin{itemize}
item[10.] What is the mechanism of subatomic decays and
scattering?
end{itemize}
end{quote}
begin{quote}
{ sf begin{itemize}
item[11.] Can the four fundamental interactions be unified， as
Einstein hoped?
end{itemize}
end{quote}
medskip
noindent{ bf Objectives and guiding principles}
medskip
The objectives of this book are
begin{enumerate}
item to derive experimentally verifiable laws of Nature based on
a few fundamental mathematical principles， and item to provide
new insights and solutions to some outstanding challenging
problems of theoretical physics， including those mentioned above.
end{enumerate}
The main focus of this book is on the symbiotic interplay between
theoretical physics and advanced mathematics. Throughout the
entire history of science， the searching for mathematical
representations of the laws of Nature is built upon the believe
that the Nature speaks the language of Mathematics. The Newton''s
universal law of gravitation and laws of mechanics are clearly
among the most important discoveries of the mankind based on the
interplay between mathematics and natural sciences. This viewpoint
is vividly revealed in Newton''s introduction to the third and
final volumes of his great Principia Mathematica: ``{ it I now
demonstrate the frame of the system of the world.}"
It was， however， to the credit of Albert Einstein who envisioned
that the laws of Nature are dictated by a few fundamental
mathematical principles. Inspired by the Albert Einstein''s vision，
our general view of Nature is synthesized in two guiding
principles， Principles~ ref{pr1.1} ref{pr1.2}， which can be
recapitulated as follows:
begin{quote}
{ it Nature speaks the language of Mathematics{ rm :} the laws of Nature 1 are represented by mathematical equations，
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