Consider a compound quark specified by its quark coefficients $n$. The following numbers may also used to characterize and identify the particle. They are all integer multiples of one eighth: they are quantized. So they are called quantum numbers.
| Characteristic | Definition |
| helicity | $\delta _{z} \equiv \begin{cases} +1 \ \ &\sf{\text{if}} \ \ &\it{n}^{\mathsf{\bar{u}}} > \it{n}^{\mathsf{u}} \\ \ \ 0 \ \ &\sf{\text{if}} \ \ &\it{n}^{\mathsf{\bar{u}}} = \it{n}^{\mathsf{u}} \\ -1 &\sf{\text{if}} \ \ &\it{n}^{\bar{\mathsf{u}}} < \it{n}^{\mathsf{u}} \end{cases}$ |
| spin | $\sigma \equiv \left| N^{\, \mathsf{U}} - N^{\, \mathsf{D}} \vphantom{\sum^{2}} \right| \, /8$ |
| charge | $q\equiv \left( {\Delta}n^{\mathsf{T}}-{\Delta}n^{\mathsf{B}}+{\Delta}n^{\mathsf{C}}-{\Delta}n^{\mathsf{S}} \vphantom{\sum^{2}} \right)/8$ |
| lepton number | $L\equiv \left( {\Delta}n^{\mathsf{G}}-{\Delta}n^{\mathsf{E}}+{\Delta}n^{\mathsf{M}}-{\Delta}n^{\mathsf{A}} \vphantom{\sum^{2}} \right)/8$ |
| baryon number | $B\equiv \left( {\Delta}n^{\mathsf{T}}-{\Delta}n^{\mathsf{B}}-{\Delta}n^{\mathsf{C}}+{\Delta}n^{\mathsf{S}} \vphantom{\sum^{2}} \right) / 8$ |
| strangeness | $S\equiv \left( {\Delta}n^{\mathsf{D}}-{\Delta}n^{\mathsf{U}}- \left| n^{\mathsf{u}}-n^{\mathsf{\bar{d}}} \vphantom{\sum^{2}} \right| + \left| n^{\mathsf{d}}-n^{\mathsf{\bar{u}}} \vphantom{\sum^{2}} \right| \,\, \right) /8$ |
| Particle Type | Definition |
| a lepton | $B = 0$ and $L \ne 0$ |
| a baryon | $B \ne 0$ and $L = 0$ |
| a meson | $B = 0$ and $L = 0$ |
| a neutral particle | $q = 0$ |
| a charged particle | $q \ne 0$ |
| a strange particle | $S \ne 0$ |
Particles can also be classified according to these characteristics as noted in the accompanying table. Attributes and identities are quantized because fundamentaly WikiMechanics is based on a finite categorical scheme of binary distinctions. Any characteristic defined from quark coefficients is necessarily quantized because quark coefficents are always integers.
Theorem: the the net number of quarks in particle $\sf{P }$ and its anti-particle $\bar{\sf{P}}$ are related as
$\rm{\Delta} \it{n} ^{\sf{Z}} \sf{(} \: \sf{P} \, \sf{)}= - \rm{\Delta} \it{n}^{\sf{Z}} \sf{(} \; \bar{\sf{P}} \: \sf{)}$
so the charge, strangeness, lepton and baryon numbers of particles and anti-particles have the same absolute value, but opposite signs.
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Next step: conservation laws. |
