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

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

 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
page revision: 528, last edited: 01 Dec 2017 21:52