Mathematical Principles of Theoretical Physics

5.5. STRUCTURE OF MEDIATOR CLOUDS AROUND SUBATOMIC PARTICLES 313

providing strong interaction potentials. In Section4.5, we have discussed problem 2). Here,
we consider problem 1).
Experiments showed that there are eight field particles for the strong interaction, called
gluons, which are massless and electric neutral, denoted by

(5.5.9) gk, 1 ≤k≤ 8.

The QCD theory shows that the gluons are vector bosons with spinJ=1.
Based on both the unified field theory and the weakton model, corresponding to the vector
gluons (5.5.9) there are eight dual field particles, which are scalar bosons with spinJ=0,
denoted by

(5.5.10) gk 0 , 1 ≤k≤ 8.

In addition, by PID, it follows from (5.5.7)-(5.5.8) that the field equations describing the
eight vector gluons (5.5.9) read

∂νSkμ ν−

gs

̄hc

fijkgα βSiα μSβj−gsQkμ= (∂μ+

gs

hc ̄

αlSlμ−

1

4

(5.5.11) α 0 xμ)φsk,

for 1≤k≤8, and the field equations describing the eight scalar gluons(5.5.10) are

∂μ∂μφsk+∂μ

[(

gs

hc ̄

αlSlμ−

1

4

α 0 xμ

)

φsk

]

=−gs∂μQkμ−

gs

hc ̄

(5.5.12) fijkgα β∂μ(Sα μi Sβj),

for 1≤k≤8, whereαl( 1 ≤l≤ 8 )andα 0 are parameters, and

Qkμ=qγμλkq (λk=λk,γμ=gμ νγν).

The field equations (5.5.11) and (5.5.12) are as in (4.4.34) and (4.4.37).
From (5.5.11) and (5.5.12) we can deduce the following theoretical conclusions for the
gluons (5.5.9) and dual gluons (5.5.10):

1) The field functionsWμk( 1 ≤k≤ 8 )describing the gluons (5.5.9) are vector fields, and,

therefore,gkin (5.5.9) are vector bosons with spinJ=1;

2) The field functionφsk( 1 ≤k≤ 8 )describing the gluons (5.5.10) are scalar fields, and

thereforegk 0 in (5.5.10) are scalar bosons withJ=0;

3) The field equations (5.5.11) and (5.5.12) are nonlinear. Consequently, the gluonsgk

andgk 0 are not in free states, and in their bound states the masses ofgkandgk 0 may

appear;

4) In the bound states, the masses can be generated by the spontaneous symmetry breaking

in (5.5.11) and (5.5.12), and the mass terms forgkandgk 0 are as follows

gk:

gs

̄hc

αlφ ̃skSlμ (φ ̃lk are the ground states),

gk 0 :α 0 Φks;