Mathematical Principles of Theoretical Physics

244 CHAPTER 4. UNIFIED FIELD THEORY

4.Basic properties of field particles.From (4.6.43)-(4.6.46) we can obtain some basic

information for the bosons as follows:

W±: spinJ= 1 , electric charge=±e, massmW,

Z: spinJ= 1 , electric charge= 0 , massmZ,

H±: spinJ= 0 , electric charge=±e, massm+H,

H^0 : spinJ= 0 , electric charge= 0 , massm^0 H.

Remark 4.21.Under the translation

Zμ→Zμ+

1

4

(mHc

h ̄

) (^21)
k^2 Z
xμ,
Wμ±→Wμ±+

1

4

(

mHc

h ̄

)^2

1

kW^2

xμ,

the equations (4.6.50) and (4.6.52) become

(4.6.53)

Zμ+k^2 ZZμ=−gwJ^0 μ,

Wμ±+k^2 WWμ±=−gwJμ±.

Similarly, if we take the gauge fixing equations

xμ∂μφa= 0 for 1≤a≤ 3 ,

instead of (4.6.42), then under the conditions

Wμa= 0 for 1≤a≤ 3 ,

the equations (4.6.46) and (4.6.45) are in the form

(4.6.54)

H^0 +

(m

Hc

h ̄

) 2

H^0 =gw∂μJ^0 μ,

H±+

(m

Hc

h ̄

) 2

H±=gw∂μJμ±.

The equations (4.6.53) and (4.6.54) are the standard Klein-Gordon models describing the
W±,Z,H±,H^0 bosons, which are derived only by the PID-PRI unified field model.

4.6.5 Introduction to the classical electroweak theory

In comparison with the PID-PRI weak interaction theory, in this subsection we briefly intro-

duce the classicalU( 1 )×SU( 2 )electroweak theory; see among many others (Kaku, 1993 ;

Griffiths, 2008 ;Quigg, 2013 ).