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Quantum Numbers

Nuclear Quantum Numbers
total angular momentum

 \textsl{ \textsf{J} } \equiv   \dfrac{ \, \left| \,  N^{\mathsf{U}}   - N^{\mathsf{D}} \, \right| \, }{8}


 q \equiv \dfrac{ {\Delta}n^{\mathsf{T}}-{\Delta}n^{\mathsf{B}}+{\Delta}n^{\mathsf{C}}-{\Delta}n^{\mathsf{S}}  }{8}

lepton number

  L\equiv \dfrac{ {\Delta}n^{\mathsf{G}}-{\Delta}n^{\mathsf{E}}+{\Delta}n^{\mathsf{M}}-{\Delta}n^{\mathsf{A}}    }{8}

baryon number

 B\equiv \dfrac{ {\Delta}n^{\mathsf{T}}-{\Delta}n^{\mathsf{B}}-{\Delta}n^{\mathsf{C}}+{\Delta}n^{\mathsf{S}}   }{ 8 }


 S \equiv \dfrac{ {\Delta}n^{\mathsf{D}}-{\Delta}n^{\mathsf{U}}- \left| n^{\mathsf{u}}-n^{\overline{\mathsf{d}}} \right| + \left| n^{\mathsf{d}}-n^{\mathsf{\overline{u}}} \right| \, }{8}

Quantum numbers are used to identify and classify particles. They are utilized in both atomic and nuclear physics. We start with the nuclear numbers which are determined from quark coefficients noted by  n. Recall that quark-coefficients are always integers. So the quantum numbers defined in the adjacent table are all integer multiples of one eighth. They are quantized, thus their name. In general, attributes and identities are quantized because EthnoPhysics is fundamentally based on a finite categorical scheme of binary distinctions. Any characteristic defined using a quark coefficient is necessarily quantized because quark coefficients are always integers.

Recall that for any seed Z, the net number of quarks in particle  \mathsf{P } and its anti-particle \overline{\mathsf{P}} are related as

\Delta n ^{\mathsf{Z}} \left( \mathsf{P} \right) = - \Delta  n^{\mathsf{Z}}  \left(  \mathsf{\overline{P}} \right)

This relationship implies that the charge, strangeness, lepton-number and baryon-number of particles and anti-particles have the same absolute value, but opposite signs

q \left( \mathsf{P} \right) = - q  \left(  \mathsf{\overline{P}} \right)

L \left( \mathsf{P} \right) = - L  \left(  \mathsf{\overline{P}} \right)

B \left( \mathsf{P} \right) = - B  \left(  \mathsf{\overline{P}} \right)

S \left( \mathsf{P} \right) = - S  \left(  \mathsf{\overline{P}} \right)

But exchanging quarks for anti-quarks does not alter thermodynamic seed counts, so for the angular momentum quantum number \textsl{\textsf{J}} \left( \mathsf{P} \right) = \textsl{\textsf{J}} \left( \mathsf{\overline{P}} \right). Particles can be classified by these quantum numbers into a few general categories as noted in the accompanying table.

Nuclear Particle Types
a boson \textsl{\textsf{J}} = \textsf{an integer}
a fermion  \textsl{\textsf{J}} = \textsf{an integer} + \frac{1}{2}
a lepton B = 0 \textsf{ and } L \neq 0
a baryon B \neq 0 \textsf{ and } L = 0
a meson B=0 \textsf{ and } L=0
a neutral particle q=0
a charged particle q \neq 0
a strange particle S \neq 0

Quarks are conserved. So the overall quantity of each quark-type in any given description may not change. Whenever some generic compound quarks  \mathbb{X},  \mathbb{Y} and   \mathbb{Z} interact, if \mathbb{X} + \mathbb{Y} \leftrightarrow \mathbb{Z} then the coefficients for any sort of quark  \mathsf{q} are related as

n^{\sf{q}} \left( \mathbb{X} \right) + n^{\sf{q}} \left( \mathbb{Y} \right) = n^{\sf{q}} \left( \mathbb{Z} \right)

But the lepton number, for example, is defined in the table above from sums of quark coefficients. So by the associative properties of addition we have

L ^{ \mathbb{X} } + L ^{ \mathbb{Y} } = L ^{ \mathbb{Z} }

Therefore the lepton number is conserved. By the same reasoning the baryon number and charge are conserved too, so

 B ^{ \mathbb{X} } + B ^{ \mathbb{Y} } = B ^{ \mathbb{Z} }


 q ^{ \mathbb{X} } + q ^{ \mathbb{Y} } = q ^{ \mathbb{Z} }

But the strangeness and angular momentum quantum-numbers are defined using absolute-value functions which are not generally associative. So   \textsl{\textsf{J}} and  S are not always conserved when compound quarks are formed or decomposed. Next we consider another property of compound quarks, their enthalpy.

Quantum numbers are related to counting quarks, which is like counting the beads in this woven panel from Borneo.
Baby Carrier Panel, Basap people. Borneo 19th century, 30 x 21 cm. Photograph by D Dunlop.