Mathematical Principles of Theoretical Physics

2 CHAPTER 1. GENERAL INTRODUCTION

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.

6. Baryon asymmetry: Where are there more particles than anti-particles?

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.

7. Are there weak and strong interaction/force formulas?

We know that the Newton and the Coulomb formulas are basic force formulas for grav-
itational 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.

8. What is the strong interaction potential of nucleus? Can we derive the
   Yukawa potential from first principles?


9. Why do leptons not participate in the strong interaction?


10. What is the mechanism of subatomic decays and scattering?


11. Can the four fundamental interactions be unified, as Einstein hoped?

2.1.1 General guiding principles

The objectives of this book are

1) to derive experimentally verifiable laws of Nature based on a few fundamental mathe-

matical principles, and

2. to provide new insights and solutions to some outstandingchallenging problems of
   theoretical physics, including those mentioned above.
   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 mathemat-
   ical 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 mechan-
   ics 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: “I now demon-
   strate 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, Principles2.1&
   2.2, which can be recapitulated as follows:

Nature speaks the language of Mathematics: the laws of Nature 1) are repre-

sented by mathematical equations, 2) are dictated by a few fundamental princi-

ples, and 3) always take the simplest and aesthetic forms.