iv
2015a,2014h), and the principle of symmetry-breaking (PSB) (Ma and Wang,2014a).
Basically, PID takes the variation of the Lagrangian actionunder the energy-momentum
conservation constraints. For gravity, PID is the direct consequence of the presence of dark
energy and dark matter. For the weak interaction, PID is the requirement of the presence of
the Higgs field. For the strong interaction, we demonstratedthat PID is the consequence of
the quark confinement phenomena.
PRI requires that the gauge theory be independent of the choices of the representation
generators. These representation generators play the samerole as coordinates, and in this
sense, PRI is a coordinate-free invariance/covariance, reminiscent of the Einstein principle of
general relativity. In other words, PRI is purely a logic requirement for the gauge theory.
PSB offers an entirely different route of unification from the Einstein unification route
which uses large symmetry group. The three sets of symmetries — the general relativistic
invariance, the Lorentz and gauge invariances, as well as the Galileo invariance — are mu-
tually independent and dictate in part the physical laws in different levels of Nature. For a
system coupling different levels of physical laws, part of these symmetries must be broken.
These three new principles have profound physical consequences, and, in particular, pro-
vide a new route of unification for the four interactions:
1) the general relativity and the gauge symmetries dictate theLagrangian;
2) the coupling of the four interactions is achieved through PID and PRI in
the unified field equations, which obey the PGR and PRI, but break sponta-
neously the gauge symmetry;
3) the unified field model can be easily decoupled to study individual interac-
tion, when the other interactions are negligible; and6.5.4 Unified field model coupling matter fields.
The main part of this book is to establish such a field theory, and to provide explanations
and solutions to a number of challenging problems and mysteries such as those mentioned
above.
Another part of the book is on building aphenomenologicalweakton model of elementary
particles, based on the new field theory that we established. This model explains all the
subatomic decays and scattering, and gives rise to new insights on the structure of subatomic
particles.
Our new field theory is based solely on a few fundamental principles. It agrees with all
the related experiments and observations, and solves many challenging problems in modern
physics. In this sense, it should reflect the truth of the Nature!
In retrospect, most attempts in modern physics regarding tothe challenges and mysteries
mentioned earlier focus on modifying,on an ad hoc basis, the basic Lagrangian actions.
Even with careful tuning, these artificial modifications often lead to unsolvable difficulties
and confusions on model-building and on the understanding of the related phenomena. The
PID approach we discovered is the first principle approach, required by the phenomena as
the dark matter, dark energy, quark confinement, and the Higgs field. It leads to dual fields,
which are not achievable by other means. Hence we believe that this is the very reason behind
the confusions and challenges that modern physics has facedfor many decades.
Chapter 1 , General Introduction, is written for everyone. It synthesizes the main ideas
and results obtained in this book. Chapter 2 develops the general view and basic physical