Mathematical Principles of Theoretical Physics
4.3. UNIFIED FIELD MODEL BASED ON PID AND PRI 207 4.3.4 Potentials of the weak and strong forces It is known that theU( 1 )gauge ...
208 CHAPTER 4. UNIFIED FIELD THEORY The weak and strong forces are given by (4.3.45) weak force: Fw=−gw∇W 0 , weak magnetic forc ...
4.4 Duality and decoupling of Interaction Fields. forms: Coulomb gauge : ∂A 1 ∂x^1 + ∂A 2 ∂x^2 + ∂A 3 ∂x^3 = 0 , Lorentz gauge : ...
210 CHAPTER 4. UNIFIED FIELD THEORY energy phenomena, the formulas of the weak and strong forces, the quark confinement, the asy ...
4.4. DUALITY AND DECOUPLING OF INTERACTION FIELDS 211 then there must exist a dual graviton with spinJ=1. In fact, for all inter ...
212 CHAPTER 4. UNIFIED FIELD THEORY 1.Gravitons and dual gravitons.It is known that as the equations describing field parti- cle ...
4.4. DUALITY AND DECOUPLING OF INTERACTION FIELDS 213 represents the force due to the nonlinear coupling ofgμ νand its dualφ. Fo ...
214 CHAPTER 4. UNIFIED FIELD THEORY sion of the classical Maxwell equations, which are expressed as (4.4.21) 1 c ∂H ∂t =−curlE, ...
4.4. DUALITY AND DECOUPLING OF INTERACTION FIELDS 215 2.Electromagnetic force. If we consider the electromagnetic force, then th ...
216 CHAPTER 4. UNIFIED FIELD THEORY 4.4.4 Strong interaction field equations The decoupled strong interaction field model from ( ...
4.4. DUALITY AND DECOUPLING OF INTERACTION FIELDS 217 Strong force. The strong interaction forces are governed by the field equ ...
218 CHAPTER 4. UNIFIED FIELD THEORY 1.Duality between W±,Z Bosons and Higgs Bosons H±,H^0 .The three massive vector bosons, deno ...
4.5. STRONG INTERACTION POTENTIALS 219 be the strong charge potential of this particle. Then the strong force between two elemen ...
220 CHAPTER 4. UNIFIED FIELD THEORY where φs=ρkφsk, Qμ=ρkQkμ, λij=ρkλijk, Sμ ν=∂μSν−∂νSμ+ gs hc ̄ λijSiμSνj. Based on the superp ...
4.5. STRONG INTERACTION POTENTIALS 221 whereδ(r)is the Dirac delta function,θμj is a constant tensor, inversely proportional to ...
222 CHAPTER 4. UNIFIED FIELD THEORY whereAis a constant given by A= k 02 cτ κ 4 with physical dimension 1 L . AssumeΦs=Φs(r)is r ...
4.5. STRONG INTERACTION POTENTIALS 223 which is a dimensionless function, and (4.5.26) βis inversely proportional to the particl ...
224 CHAPTER 4. UNIFIED FIELD THEORY which is the strong attraction radius of nucleons, and Qkμ=qγμτkq (τk=τk). Let the strong in ...
4.5. STRONG INTERACTION POTENTIALS 225 andφ(r)is as in (4.5.36). In summary, for a particle withNstrong charges and radiusρ, its ...
226 CHAPTER 4. UNIFIED FIELD THEORY 4.5.3 Quark confinement Quark model was confirmed by lots of experiments. However, noany sin ...
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