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.
| Quantum Number | Definition |
| total angular momentum | $\begin{align} 𝘑 \equiv \frac{ \, \left| \, N^{\mathsf{U}} - N^{\mathsf{D}} \, \right| \, }{8} \end{align}$ |
| charge | $\begin{align} q \equiv \frac{ {\Delta}n^{\mathsf{T}}-{\Delta}n^{\mathsf{B}}+{\Delta}n^{\mathsf{C}}-{\Delta}n^{\mathsf{S}} }{8} \end{align}$ |
| lepton number | $\begin{align} L\equiv \frac{ {\Delta}n^{\mathsf{G}}-{\Delta}n^{\mathsf{E}}+{\Delta}n^{\mathsf{M}}-{\Delta}n^{\mathsf{A}} }{8} \end{align}$ |
| baryon number | $\begin{align} B\equiv \frac{ {\Delta}n^{\mathsf{T}}-{\Delta}n^{\mathsf{B}}-{\Delta}n^{\mathsf{C}}+{\Delta}n^{\mathsf{S}} }{ 8 } \end{align}$ |
| strangeness | $\begin{align} S\equiv \frac{ {\Delta}n^{\mathsf{D}}-{\Delta}n^{\mathsf{U}}- \left| n^{\mathsf{u}}-n^{\bar{\mathsf{d}}} \right| + \left| n^{\mathsf{d}}-n^{\mathsf{\bar{u}}} \right| \, }{8} \end{align}$ |
| Particle Type | Definition |
| a boson | $𝘑 = \sf{an \ integer}$ |
| a fermion | $𝘑 = \sf{ \text{an integer plus one half}}$ |
| 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 fundamentally 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 net number of quarks in particle $\sf{P }$ and its anti-particle $\overline{\sf{P}}$ are related as
$\rm{\Delta} \it{n} ^{\sf{Z}} \left( \sf{P} \right) = - \rm{\Delta} \it{n}^{\sf{Z}} \left( \sf{\overline{P}} \right)$
so the charge, strangeness, lepton-number and baryon-number of particles and anti-particles have the same absolute value, but opposite signs
$q \left( \sf{P} \right) =- q \left( \sf{\overline{P}} \right)$ $L \left( \sf{P} \right) =- L \left( \sf{\overline{P}} \right)$ $B \left( \sf{P} \right) = -B \left( \sf{\overline{P}} \right)$ $S \left( \sf{P} \right) =- S \left( \sf{\overline{P}} \right)$
But exchanging quarks for anti-quarks does not alter thermodynamic seed counts, so for the angular momentum
$𝘑 \left( \sf{P} \right) = 𝘑 \left( \sf{\overline{P}} \right)$
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Quantum Numbers |
| Summary |
| Adjectives | Definition | |
| Quantum Numbers | $\sf{\text{Numbers used to identify particles.}}$ | 4-10 |
| Adjective | Definition | |
| Total Angular Momentum Quantum Number | $\begin{align} 𝘑 \equiv \frac{ \, {\large{\mid}} \, N^{\mathsf{U}} \! -N^{\mathsf{D}} {\large{\mid}} \, }{8} \end{align}$ | 4-11 |
| Adjective | Definition | |
| Charge | $\begin{align} q \equiv \frac{ {\Delta}n^{\mathsf{T}}-{\Delta}n^{\mathsf{B}}+{\Delta}n^{\mathsf{C}}-{\Delta}n^{\mathsf{S}} }{8} \end{align}$ | 4-12 |
| Adjective | Definition | |
| Lepton Number | $\begin{align} L\equiv \frac{ {\Delta}n^{\mathsf{G}}-{\Delta}n^{\mathsf{E}}+{\Delta}n^{\mathsf{M}}-{\Delta}n^{\mathsf{A}} }{8} \end{align}$ | 4-13 |
| Adjective | Definition | |
| Baryon Number | $\begin{align} B\equiv \frac{ {\Delta}n^{\mathsf{T}}-{\Delta}n^{\mathsf{B}}-{\Delta}n^{\mathsf{C}}+{\Delta}n^{\mathsf{S}} }{ 8 } \end{align}$ | 4-14 |
| Adjective | Definition | |
| Strangeness | $\begin{align} S\equiv \frac{ {\Delta}n^{\mathsf{D}}-{\Delta}n^{\mathsf{U}}- \mid n^{\mathsf{u}}-n^{\bar{\mathsf{d}}} \mid + \mid n^{\mathsf{d}}-n^{\mathsf{\bar{u}}} \mid \, }{8} \end{align}$ | 4-15 |
| Noun | Definition | |
| Lepton | $B=0 \ \ \text{and} \ \ L \ne 0$ | 4-16 |
| Noun | Definition | |
| Baryon | $B \ne 0 \ \ \text{and} \ \ L = 0$ | 4-17 |
| Noun | Definition | |
| Meson | $B=0 \ \ \text{and} \ \ L = 0$ | 4-18 |
| Noun | Definition | |
| Neutral Particle | $q=0$ | 4-19 |
| Noun | Definition | |
| Boson | $𝘑 \, = \sf{\text{ an integer}}$ | 4-20 |
| Noun | Definition | |
| Fermion | $𝘑 \, = \sf{\text{ an integer plus one half}}$ | 4-21 |
