Mathematical Principles of Theoretical Physics

5.1. BASIC KNOWLEDGE OF PARTICLE PHYSICS 257

The main quantum numbers of particles are:

(5.1.2)

massm, electric chargeQ, lifetimeτ,

spinJ, lepton numberL, baryon numberB,

parityπ, isospin(I,I 3 ), strange numberS,

G-parity, hyperchargeY.

In addition, there are some new quantum numbers, including the weak chargeQw, strong
chargeQs, and colour indexk, which play an important role in in the weakton model intro-
duced in Section5.3.
We now briefly introduce the quantum numbers listed in (5.1.2).

1 Mass. This is a quantity to characterize the inertia, and also plays the role of gravita-
tional charge. In the macro-world, masses are continuous indistribution, however in quantum
world masses are discrete. The same particles have the same masses, but the different massive
particles have a gap between their masses.
In non-quantum physics, the masses are additive, i.e. if a body A consists of two bodies
BandC, then the massmAofAis the sum of massesmBandmCofBandC:

(5.1.3) A=B+C⇒mA=mB+mC.

But, the additive relation (5.1.3) is not valid in a quantum system.
Mass is a most important quantum number, which plays a role ofan identity card for all
massive particles.

2.Electric charge Q.This is an important quantum number. It is the source of electro-
magnetic force. In the four interaction charges:m,e,gw,gs, the electric chargeeis unique
one possessing positive and negative values. The electric charges are discrete, they appear
only at an integral multiples of the electron chargee:^1

Q=±ne (n= 0 , 1 , 2 ,···).

Electric charge is an additive conservation quantity. For any particle reaction:

A 1 +···+An→B 1 +···BN,

we have
n
∑
k= 1

QAk=

N

∑

k= 1

QBk,

whereQAkandQBkare the electric charges of particlesAkandBk

3.Lifetime of particles.Due to the decay property for most particles, the lifetime becomes
a quantum number. Except the long lifetime particles: the electrone, protonp, neutrinov,
photonγ, gluongk, gravitonG, all other particles undergo decays.

(^1) In the weakton model of elementary particles,w∗carries 2/3 electric charge, andw 1 andw 2 carry− 1 /3 and
− 2 /3 electric charges respectively.