Mathematical Principles of Theoretical Physics

6.4. ENERGY LEVELS OF SUBATOMIC PARTICLES 367 In Section6.4.1we see that charged leptons and quarks are made up of three weakton ...

368 CHAPTER 6. QUANTUM PHYSICS λkis independent ofj( 1 ≤j≤ 3 ), i.e. each weakton has the same bound energyλkbut in different bo ...

6.4. ENERGY LEVELS OF SUBATOMIC PARTICLES 369 where^12 mv^2 is the kinetic energy of each weakton in electronrethe radius of the ...

370 CHAPTER 6. QUANTUM PHYSICS 6.4.4 Baryons and mesons Hadrons include baryons and mesons, their spectral equations are given r ...

6.4. ENERGY LEVELS OF SUBATOMIC PARTICLES 371 By (6.4.7), the strong interaction potential for quarks is taken as (6.4.50) S 0 = ...

372 CHAPTER 6. QUANTUM PHYSICS i.e.gwandgshave the same order. Therefore, the interactions for the gluon are both weak and stron ...

6.4. ENERGY LEVELS OF SUBATOMIC PARTICLES 373 Each energy levelEkcan be expressed as (6.4.60) Ek=E 0 +λk ( 1 ≤k≤N), whereE 0 is ...

374 CHAPTER 6. QUANTUM PHYSICS the spectral equations for charged leptons and quarks are given by (6.4.42), and which are writte ...

6.4. ENERGY LEVELS OF SUBATOMIC PARTICLES 375 This number is very large because(ρn/ρw)≥ 105. We remark that the estimate (6.4.67 ...

376 CHAPTER 6. QUANTUM PHYSICS Hence, it is natural to think that Bwργ ρw = ργ ρ = 102 ∼ 104. Thus, by (6.4.71) and (6.4.6) we g ...

6.5. FIELD THEORY OF MULTI-PARTICLE SYSTEMS 377 then from (6.4.74) we derive that ∆E= 10 −^40 ̄hc/cm= 2 × 10 −^45 eV. This is a ...

378 CHAPTER 6. QUANTUM PHYSICS By using coordinatexkto represent the particleAkamounts essentially to saying that the wave func ...

6.5. FIELD THEORY OF MULTI-PARTICLE SYSTEMS 379 whereψ 1 ,···,ψNare the wave functions of the N particles. We now need to explai ...

380 CHAPTER 6. QUANTUM PHYSICS The main motivation to introduce Postulates6.25and6.26are as follows. Consider an N-particle syst ...

6.5. FIELD THEORY OF MULTI-PARTICLE SYSTEMS 381 Fermionic systems ConsiderNfermions at the same level with interaction chargeg, ...

382 CHAPTER 6. QUANTUM PHYSICS Thus, by (6.5.18) and (6.5.19) we derive the field equations of theN-particle system (6.5.15)-(6. ...

6.5. FIELD THEORY OF MULTI-PARTICLE SYSTEMS 383 and the mass matrix is given by (6.5.16). The action is (6.5.25) L= ∫ (LG+LKG)dx ...

384 CHAPTER 6. QUANTUM PHYSICS Namely,LDandLKGare given by LD=Ψ [ iγμ ( ∂μ+ in 1 g hc ̄ G^0 μ+ in 1 g hc ̄ G ̃μ+in^1 g ̄hc Gaμτa ...

6.5. FIELD THEORY OF MULTI-PARTICLE SYSTEMS 385 B 1 j,···,BNj: (6.5.34) at levelA: A={A 1 ,···,AK}, at levelB: Aj={B 1 j,···,BNj ...

386 CHAPTER 6. QUANTUM PHYSICS However, if we consider the interaction potentials betweenthe particles ofN-particle systems, the ...