Mathematical Principles of Theoretical Physics

26 CHAPTER 1. GENERAL INTRODUCTION

This mechanism can also be applied to supernovae explosion.When a very massive red

giant completely consumes its central supply of nuclear fuels, its core collapses. Its radiusr 0

begins to decrease, and consequently theδ-factor increases. The huge massmand the rapidly

reduced radiusr 0 make theδ-factor approaching one. The thermal convection gives riseto

an outward radial circulation momentum fluxPr. Then the radial force as in (1.10.3) will lead

to the supernova explosion. Also,Pr=0 atr=r 0 , wherer 0 is the radius of blackhole core of

supernovae. Consequently, the supernova’s huge explosionpreserves a smaller ball, yielding

a neutron star.

1.11 Multi-Particle Systems and Unification

The field theory for multi-particle system was discovered by(Ma and Wang,2014d). Clas-

sical quantum dynamic equations describe single particle systems. The existing model for a

multi-particle system is non-relativistic and is based on prescribing the interaction between

particles using such potentials as the Coulomb potential.

As far as we know, there is still no good model for a multi-particle system, which takes

also into consideration the dynamic interactions between particles. The main obstacle for es-

tablishing a field theory for an interacting multi-particlesystem is the lack of basic principles

to describe the dynamic interactions of the particles.

Basic postulates for interacting multi-particle systems

To seek the needed principles, we proceed with three observations.

1. One natural outcome of the field theory of four interactions developed recently by
   the authors and addressed in the previous sections is that the coupling constants for the
   U( 1 )×SU( 2 )×SU( 3 )gauge theory play the role of the three chargese,gwandgsfor elec-
   tromagnetism, the weak and the strong interaction. These charges generate interacting fields
   among the interacting particles.
   Now we consider anN-particle system with each particle carrying an interaction charge
   g. Let this be a fermionic system, and the Dirac spinors be given by

Ψ= (ψ 1 ,···,ψN)T,

which obeys the Dirac equations:

(1.11.1) iγμDμΨ+MΨ= 0 ,

whereMis the mass matrix, and

(1.11.2) DμΨ=∂μΨ+igGΨ,

whereG= (Gijμ)is an Hermitian matrix, representing the interacting potentials between the

N-particles generated by the interaction chargeg.

Now let

{τ 0 ,τ 1 ,···,τK|K=N^2 − 1 }