Conservation Laws for Particles
//Bead Panel// from a baby carrier, Basap people, Borneo 19th century, 30 x 21 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop.
Bead Panel from a baby carrier, Basap people, Borneo 19th century, 30 x 21 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop.

Quarks are indestructible 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 quark coefficients $n$ of any sort of quark 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 from sums and differences of quark coefficients. So by the associative propertiesXlink.png of addition and subtraction

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

and we say that the lepton number is conserved. By the same reasoning the baryon number and charge are conserved too so that

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

and

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

But the strangeness and spin are defined using absolute-value functions which are not generally associative. So spin and strangeness are not always conserved when compound quarks are formed or decomposed. Overall, baryon-number, lepton-number and charge are quantized and conserved because quarks are quantized and conserved. Similarly, the internal energy $U$ of each quark has a specific fixed value, so

$U ^{ \mathbb{X} } + U ^{ \mathbb{Y} } = U ^{ \mathbb{Z} }$

and internal energy is conserved whenever particles are combined or decomposed.

Right.png Next step: building quark models of particles.
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License