Mathematical Principles of Theoretical Physics

5.4. MECHANISMS OF SUBATOMIC DECAYS AND ELECTRON RADIATIONS 307 It is clear that the final particles are the protonpand mesonπ+. ...

308 CHAPTER 5. ELEMENTARY PARTICLES The weakton constituents of this decay is given by (w∗w 2 w 2 )(w∗w 1 w 1 )(cu)+w∗w∗(gk)+ 2 ...

5.4. MECHANISMS OF SUBATOMIC DECAYS AND ELECTRON RADIATIONS 309 There are three exchange processes in (5.4.32): (5.4.33) gk+γ+γ ...

310 CHAPTER 5. ELEMENTARY PARTICLES γ,γ 0 ,gk,gk 0 ,ν, is given by Fw=−gw(ρm)gw(ρe) ∂ ∂r [ 1 r e−kr− B ̃ ρ ̃ ( 1 + 2 kr)e−^2 kr ...

5.5.5 Mediator clouds of subatomic particles e F (a) e γ (b) γ Figure 5.15: (a) The naked electron is accelerated or decelerated ...

312 CHAPTER 5. ELEMENTARY PARTICLES and antiparticles have three anti-colors: (5.5.3) anti-redr, anti-greeng, anti-blueb. Based ...

5.5. STRUCTURE OF MEDIATOR CLOUDS AROUND SUBATOMIC PARTICLES 313 providing strong interaction potentials. In Section4.5, we have ...

314 CHAPTER 5. ELEMENTARY PARTICLES 5) Free gluons, if there exist, are massless. Remark 5.16.Gluons and photons are massless on ...

5.5. STRUCTURE OF MEDIATOR CLOUDS AROUND SUBATOMIC PARTICLES 315 ur ug ur ̄g Figure 5.16 The reaction formula of the gluon radia ...

316 CHAPTER 5. ELEMENTARY PARTICLES 5.5.3 Color algebra The main objective of this and next subsections is to introduce a consis ...

5.5. STRUCTURE OF MEDIATOR CLOUDS AROUND SUBATOMIC PARTICLES 317 Only two of these added color indices are independent, and infa ...

318 CHAPTER 5. ELEMENTARY PARTICLES Two remarks are now in order. Remark 5.18.Each elementω=Σnkek∈Prepresents a particle system, ...

5.5. STRUCTURE OF MEDIATOR CLOUDS AROUND SUBATOMIC PARTICLES 319 andN 1 ,N 2 are as (5.5.29) N 1 = 3 ∑ k= 1 nk, N 2 = 3 ∑ k= 1 m ...

320 CHAPTER 5. ELEMENTARY PARTICLES 3) a homomorphism Indc:PN→Gc, such that for each elementw=∑Nk= 1 nkek∈PN, we can define a co ...

5.5. STRUCTURE OF MEDIATOR CLOUDS AROUND SUBATOMIC PARTICLES 321 Definition 5.20.The w∗-color algebra is the triplet{Gc,P^3 ,Ind ...

322 CHAPTER 5. ELEMENTARY PARTICLES Theorem 5.21.The following assertions hold true for the w∗-color algebra: 1) For any gluon p ...

5.5. STRUCTURE OF MEDIATOR CLOUDS AROUND SUBATOMIC PARTICLES 323 Proof of Theorem5.21.We proceed in the following three steps. S ...

324 CHAPTER 5. ELEMENTARY PARTICLES 5.5.5 Mediator clouds of subatomic particles Subatomic particles include charged leptons, qu ...

5.5. STRUCTURE OF MEDIATOR CLOUDS AROUND SUBATOMIC PARTICLES 325 weak repelling radius of the mediators. Consequently, the total ...

326 CHAPTER 5. ELEMENTARY PARTICLES We remark that two scalar mediators can be transformed into apair of vector particles withJ= ...