Mathematical Principles of Theoretical Physics

260 CHAPTER 5. ELEMENTARY PARTICLES

the total parities of both sides of (5.1.5) are the same:

(− 1 )l^1 πA 1 ···πAN= (− 1 )l^2 πB 1 ···πBK.

In Subsection5.1.4, we shall introduce the violation of parity conservation inthe weak inter-
action in detail.

8.Isospin(I,I 3 ).The isospin was first presented in 1932 by Heisenberg, and wasused to
describe that the strong interaction between protons and neutrons, independently of electric
charges. Later, along with the development of particle physics, it was discovered that the
isospin is a good quantum number for all hadrons.
Isospin has two components(I,I 3 ), whereIis called the isospin andI 3 is the third com-
ponent of isospin. In a many-particle system, the isospinIobeys the vectorial additive rule
andI 3 obeys the usual additive rule. We shall introduce the isospin again in Subsection5.1.4.

9.Strange number S. In 1947, C. D. Rochester and C. C. Butler first discovered the
strange particleK^0 , a neutral meson, from cosmic rays, and later many strange particles such
asK±,Λ,Σ±,Ξ−,Ξ^0 ,Ω−were found. They are named the ”strange” because these particles
possess a kind quantum number called the strange number.
The strange numberSis an additive quantum number, which is conserved only in the
electromagnetic and strong interactions, and takes the integral values:

S= 0 , 1 , 2 , 3 ,···.

10.Hypercharge Y. HyperchargeYis another quantum number for hadrons, defined by

Y=S+B,

whereSandBare the strange number and the baryon number.

11.G-parity. Gparity is a conservative quantity only for strong interactions under the
G-transformation
Gψ=CeˆiπI^2 ψ,

whereCˆis the transformation of particles and antiparticles:

CAˆ =A, CˆA=A, Athe antiparticle ofA,

andI 2 is the second axis of the isospin space.

5.1.3 Particle transitions

Particle transition is the main dynamic form of sub-atomic particles, which includes particle
decays, scatterings and various radiations. It is called ”transition” because in these processes
particles will undergo a transition from an energy level to other energy levels.
The particle transition is a crucial way for us to understandthe particle structures and
properties. In particular, these transition processes canreveal the mysteries of the weak and
the strong interactions.