Preface

The objectives of this book are to derive experimentally verifiable laws of Nature based on
a few fundamental mathematical principles, and to provide new insights and solutions to a
number of challenging problems of theoretical physics. This book focuses mainly on the
symbiotic interplay between theoretical physics and advanced mathematics.
The great success and experimental verification of both Albert Einstein’s theory of rel-
ativity and quantum mechanics have placed them as cornerstones of modern physics. The
fundamental principles of both relativity and quantum mechanics are the starting point of the
study undertaken in this book.
James Clerk Maxwell’s discovery of the Maxwell equations marks the beginning of the
field theory and the gauge theory. The quantum electrodynamics (QED) is beautifully de-
scribed by theU( 1 )abelian gauge theory. The non-abelianSU(N)gauge theory was origi-
nated from the early work of (Weyl, 1919 ;Klein, 1938 ;Yang and Mills, 1954 ). Physically,
gauge invariance refers to the conservation of certain quantum property of the interacting
physical system. Such quantum property ofNparticles cannot be distinguished for the in-
teraction. Consequently, the energy contribution of theseNparticles associated with the
interaction is invariant under the generalSU(N)phase (gauge) transformations.

The success and experimental support of the gauge theory in describing the electromag-
netism, the strong and the weak interactions clearly demonstrate that the principle of gauge
invariance is indeed a principle of Nature.

We have, at our disposal, the principle of general relativity, the principle of Lorentz invari-
ance (special theory of relativity), and the principle of gauge invariance. These are symmetry
principles. We can show that these symmetry principles, together with the simplicity of laws
of Nature, dictate the actions of the four fundamental interactions of Nature: the gravity, the

4.3.4 Potentials of the weak and strong forces.

Modern theoretical physics also faces great challenges andmysteries. For example, in
astrophysics and cosmology, the most important challengesand mysteries include 1) the un-
explained dark matter and dark energy phenomena, 2) the existence and properties of black
holes, 3) the structure and origin of our Universe, and 4) themechanism of supernovae ex-
plosion and active galactic nucleus jets. In particles physics, the nature of Higgs fields, quark
confinement and the unification of four fundamental interactions are among the grand chal-
lenges.
The breakthrough of our work presented in this book and in a sequence of papers comes
from our recent discovery of three new fundamental principles: the principle of interac-
tion dynamics (PID), the principle of representation invariance (PRI) (Ma and Wang,2014e,

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