Counting Quarks
//Bead Panel// from a baby carrier, Bahau people. Borneo 20th century, 27 x 24 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop.
Bead Panel from a baby carrier, Bahau people. Borneo 20th century, 27 x 24 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop.

Let P be a generic particle composed of some collection of seeds. One way to make a mathematical description of P is just to count the number of different types of seeds in P. To satisfy Anaxagorean convention, Cantor's definition of a set, and Pauli's exclusion principle, we require that seeds are perfectly distinct. Therefore seed counts always report integers, never fractions.

If all seeds are paired in quarks, then P can also be represented as a set of quarks and mathematically described by counting quarks. We note the results of such an inventory using the symbol n. For example, if P contains three amperic quarks, we write

\mbox{\fontsize{14}{18}\selectfont $ n^{\sf{a}}=3 $}

These numbers are called quark coefficients because they can be interpreted as factors in a nuclear reaction that yields P. For example if

\mbox{\fontsize{14}{18}\selectfont $ \sf{s}+2\sf{c} \to \sf{P} $}

then the quark coefficients of P are \mbox{\fontsize{16}{16}\selectfont$ \overset{ n^{\sf{s}} = 1 }{ \textcolor{white}{\text{\_}} } $} and \mbox{\fontsize{16}{16}\selectfont$ \overset{ n^{\sf{c}} = 2 }{ \textcolor{white}{\text{\_}} } $}. Quark coefficients are always integers because seed counts are always integers and there are two seeds per quark by definition. In general, we use the symbol \mbox{\fontsize{16}{16}\selectfont$ \overset{ n^{\sf{z}} }{ \textcolor{white}{\text{\_}} } $} or \mbox{\fontsize{16}{16}\selectfont$ \overset{ n^{\zeta} }{ \textcolor{white}{\text{\_}} } $} to generically note coefficients of ordinary quarks. Recall that \mbox{\fontsize{14}{14}\selectfont$ \overset{ \zeta }{ \textcolor{white}{\text{\_}} } $} is just a number that indicates quark-type. Coefficients of anti-quarks are written with an overline as \mbox{\fontsize{16}{16}\selectfont$ \overset{ n^{\overline{\sf{z}}} }{ \textcolor{white}{\text{\_}} } $}. A few other quantities used for describing P are defined below. Z notes a thermodynamic seed, and also a quark-type.

Characteristic Definition
the total number of ζ-type quarks \mbox{\fontsize{14}{18}\selectfont $ N^{\zeta} \equiv n^{\sf{\overline{z}}} + n^{\sf{z}} $}
the total number of all types of ordinary-quarks \mbox{\fontsize{14}{18}\selectfont $ N^{\circ} \equiv \sum_{\zeta =1}^{10} n^{\zeta} $}
the proportion of ζ-type ordinary-quarks \mbox{\fontsize{14}{18}\selectfont $ \wp^{\zeta} \equiv n^{\zeta} / N^{\circ} $}
the net number of Z-type quarks \mbox{\fontsize{14}{18}\selectfont $ {\Delta}n^{\sf{Z}} \equiv n^{\sf{\overline{z}}} - n^{\sf{z}} $}
the net number of big baryonic quarks \mbox{\fontsize{14}{18}\selectfont $ \Delta n^{\sf{big}} \equiv \Delta n^{\sf{T}} + \Delta n^{\sf{B}} $}
the net number of small baryonic quarks \mbox{\fontsize{14}{18}\selectfont $ \Delta n^{\sf{small}} \equiv \Delta n^{\sf{C}} + \Delta n^{\sf{S}} $}

Theorem: The the net number of quarks in particle P and its anti-particle P are related as

\mbox{\fontsize{14}{18}\selectfont $ \rm{\Delta} \it{n} ^{\sf{Z}} \left( \sf{P} \right)= - \rm{\Delta} \it{n}^{\sf{Z}} \left( \overline{\sf{P}} \right) $}

Right.png
Next step: a more discerning description of quarks.
page_revision: 536, last_edited: 1283445353|%e %b %Y, %H:%M %Z (%O ago)
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