WikiMechanics

Usap, Sasak people. Lombok, 20th century, 46 x 52 cm. From the collection of Dr. Yong Li Lan, Singapore. Photograph by D Dunlop.

Consider a particle P described by an ordered chain of events where each orbital cycle $\sf{\Omega}$ can be expressed as a pair of events

$\sf{\Omega} = \left\{ \sf{P}_{\LARGE{\circ}} , \sf{P}_{\LARGE{\bullet}} \vphantom{Q^{2}} \right\}$

that are out of phase with each other so that

$\delta _{\theta} \left( \sf{P}_{\LARGE{\circ}} \right) =- \, \delta _{\theta} \left( \sf{P}_{\LARGE{\bullet}} \right) = \pm \rm{1}$

Then $\sf{P}_{\LARGE{\circ}}$ and $\sf{P}_{\LARGE{\bullet}}$ are called phase components of P. If these two sets are composed from the same selection of quarks, then a description of the whole cycle $\sf{\Omega}$ is unaffected if there is any confusion or mix-up about the sign of the phase. This robust indifference to the phase is useful, so we give particles like this a special name: If

$\sf{P}_{\LARGE{\circ}} = \sf{P}_{\LARGE{\bullet}}$

then we say that P has phase symmetry. The most important examples of particles with phase symmetry are protons and electrons. So it is possible to make descriptions of protons and electrons that ignore the phase. Alternatively, if $\sf{P}_{\LARGE{\circ}} = \overline{\sf{P} _{\LARGE{\bullet}}}$ then we say that P has phase anti-symmetry.

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Phase Symmetry