Identifying Particles

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
spin $\begin{align} \sigma \equiv \frac{ \, \left| \, N^{\mathsf{U}} - N^{\mathsf{D}} \, \right| \, }{8} \end{align}$
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 $\sigma = \sf{an \ integer}$
a fermion $\sigma = \sf{ \text{an integer plus one half}}$
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 spin

$\sigma \left( \sf{P} \right) = \sigma \left( \sf{\overline{P}} \right)$

Right.png Next step: conservation laws.
Summary
Adjectives Definition
Quantum Numbers $\sf{\text{Numbers used to identify particles.}}$ 4-9
Adjective Definition
Spin $\begin{align} \sigma \equiv \frac{ \, \mid N^{\mathsf{U}} - N^{\mathsf{D}} \mid \, }{8} \end{align}$ 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 $\sigma = \sf{\text{ an integer}}$ 4-20
Noun Definition
Fermion $\sigma = \sf{\text{ an integer plus one half}}$ 4-21
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