Tampan, Paminggir people. Sumatra 19th century, 70 x 70 cm. From the library of Darwin Sjamsudin, Jakarta. Photograph by D Dunlop. |

Consider a particle P characterized by some repetitive chain of events

$\Psi ^{\sf{P}} = \left( \sf{\Omega}_{1} , \sf{\Omega}_{2} , \sf{\Omega}_{3} \ \ldots \ \right)$

where each orbital cycle is some bundle of quarks

$\sf{\Omega} = \left\{ \sf{q}_{1}, \sf{q}_{2}, \sf{q}_{3} \ \ldots \ \right\}$

Let these quarks be assembled into a quark model of P that uses the radius vector $\overline{\rho}$ to describe P in quark space. Definition: the **work** done to build the model is the number

$W \equiv \rho k_{\sf{F}}$

So constructing models of centered particles requires the least work. Recall that the constant $k_{\sf{F}}$ was introduced earlier to relate the internal energy of quarks to their radii. So $W$ is just another, slightly different representation of the internal energy of the quarks in P. The square of the work done is expressed in terms of the radial components as

$W^{2} = \rho^{2} k^{2}_{\sf{F}} = \left( \vphantom{\sum^{\, 2}} \rho_{m}^{ 2} k_{mm} + \rho_{e}^{2} k_{ee} + \rho_{z}^{2} + 2 \rho_{e} \rho_{m} k_{em} + 2 \rho_{e} \rho_{z} k_{ez} + 2 \rho_{m} \rho_{z} k_{mz} \right) k^{2}_{\sf{F}}$

If extra quarks are absorbed or emitted by P, then $\sf{\Omega}$ is replaced by a new bundle $\sf{\Omega}^{\prime}$ and $W$ changes to $W^{\prime}$. The quantity $\Delta W \equiv W^{\prime} - W$ may be used to describe the change. Furthermore, since all of the quarks in a description can in principle be thought of as a single particle, an overall value of $\Delta W$ may be relevent if quarks are introduced or removed *anywhere* in a description, not just in P. Theorem: particles and anti-particles have opposing radius vectors $\overline{\rho} \left( \sf{P} \right) = - \overline{\rho} \left( \sf{\overline{P}} \right)$ but their norms are the same, so

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

and the work required to assemble any particle is the same as the work done to build its corresponding anti-particle.

Summary |

Noun | Definition | |

Work | $W \equiv \rho k_{\sf{F}}$ | 5-19 |