Mathematical Principles of Theoretical Physics
4.5. STRONG INTERACTION POTENTIALS 227 4.5.4 Asymptotic freedom The strong interaction potentials provide also a natural explana ...
228 CHAPTER 4. UNIFIED FIELD THEORY whereλis a parameter,nf=6 is the flavor number of quarks, andq^2 is the transfer momen- tum ...
4.5. STRONG INTERACTION POTENTIALS 229 while in the nucleon level, (4.5.55) nucleon strong force is repulsive in 0<r< 10 − ...
230 CHAPTER 4. UNIFIED FIELD THEORY wheregis the Yukawa strong charge, and (4.5.58) g^2 = 1 ∼ 10 hc ̄. By (4.5.57) we can deduce ...
4.5. STRONG INTERACTION POTENTIALS 231 where (4.5.63) ρn= 10 −^16 cm, kn= 1013 cm−^1. 4.Parameters Anand g^2 s.First, we use the ...
232 CHAPTER 4. UNIFIED FIELD THEORY whereβ= √ 2 / √ 8 √ e−e,gis the Yukawa charge,r 1 = 10 −^13 cm, and the modified Yukawa forc ...
4.5. STRONG INTERACTION POTENTIALS 233 4.5.7 Short-range nature of strong interaction By the layered potentials (4.5.41) for the ...
234 CHAPTER 4. UNIFIED FIELD THEORY 4.6 Weak Interaction Theory 4.6.1 Dual equations of weak interaction potentials According to ...
4.6 Weak Interaction Theory It is clear that the following state (Wμa,φwa,ψ) = ( 0 ,φ 0 a, 0 ) withφ 0 abeing constants, is a so ...
236 CHAPTER 4. UNIFIED FIELD THEORY wherecτis the wave length ofφw,Qw=−Jw 0 , andJwμis as in (4.6.5). The two dual equations (4. ...
4.6. WEAK INTERACTION THEORY 237 Thus we obtain ∂μJwμ=i gw hc ̄ ωaWμbψ γμ[σa,σb]ψ=− 2 gw ̄hc (4.6.20) εabcωaWμbJμc. Here we used ...
238 CHAPTER 4. UNIFIED FIELD THEORY Inserting (4.6.25) into (4.6.13) we get (4.6.26) −∆Φw+k 12 Φw=gwQw+ gwB ρw 1 r e−k^0 r, wher ...
4.6. WEAK INTERACTION THEORY 239 Note that the dimensions ofBandβ 0 inφ(r)are 1/LandL. The parameterB=Bβ 0 is dimensionless. Phy ...
240 CHAPTER 4. UNIFIED FIELD THEORY The weak force between the two particles is given by (4.6.33) F=− d dr V=gw(ρ 1 )gw(ρ 2 )e−k ...
4.6. WEAK INTERACTION THEORY 241 Hence, we deduce from (4.6.35) and (4.6.36) that 81 ( ρw ρn ) 6 g^2 w= 8 √ 2 ( mw mp ) 2 × 10 − ...
242 CHAPTER 4. UNIFIED FIELD THEORY To match (4.6.40) and (4.6.41), we take theSU( 2 )generator transformation as follows σ ...
4.6. WEAK INTERACTION THEORY 243 which are derived by the following transformation k^2 W k^2 W k^2 Z =√gw 2 ̄hc 1 i 0 ...
244 CHAPTER 4. UNIFIED FIELD THEORY 4.Basic properties of field particles.From (4.6.43)-(4.6.46) we can obtain some basic inform ...
4.6. WEAK INTERACTION THEORY 245 The fields in the electroweak theory are as follows: SU( 2 )gauge fields: Wμ^1 ,Wμ^2 ,Wμ^3 , U ...
246 CHAPTER 4. UNIFIED FIELD THEORY U( 1 )gauge transformation: L→e i 2 βL, φ→e− 2 iβ φ, R→eiβR, Wμa→Wμa− 2 g 2 ∂μβ, Bμ→Bμ+ 2 ...
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