Leptons as fermions

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We are not going deep into the physics of spin and spinors here! We just need the bare minimum about spin and fermions for the SysML hierarchy.
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From the SysML hierarchy point of view, the crucial thing is that a Fermion is an abstraction representing some rules for many kinds of particles, and it need not always be an elementary particle, it could be a composite particle. We therefore have to use multiple inheritance:

We do, however, have to be careful not to inherit equivalent redefined properties in twice. The spin:Spin[1]=0.5 redefinition has now been bumped up from Lepton into a reusable abstract block SpinHalfParticle, and the temporary redefinition spin:Spin[1] that was in ElementaryParticle has been removed completely.

The abstract block SpinHalfParticle carries properties and constraints that apply to any spin-1/2 particle (not just elementary particles). There are two different representations of the two possible spin states: (1) 'up' and 'down' enumeration literals within the enumeration value type SpinHalfState; (2) the allowed values +0.5 and -0.5 of the Sz spin projection component, represented by a value property sz:SpinProjection, where SpinProjection is a Real, so that - unlike 'up' and 'down' - we can easily do some maths with it. (The use of the z-axis is an arbitrary convention).

In SpinHalfParticle the value property spinState is redefined to have the type SpinHalfState. The value properties spinState and sz are then constrained using OCL:


this.spinState = SpinHalfState::up implies this.sz = 0.5 and this.spinState = SpinHalfState::down implies this.sz = -0.5

this.sz = 0.5 implies this.spinState = SpinHalfState::up and this.sz = -0.5 implies this.spinState = SpinHalfState::down

A mapping between them is controlled using SysML Parametrics. The constraint on ConstraintBlock SpinZ is written in BeanShell; it is not particularly elegant, but works fine when run in Cameo Systems Modeler® or Cameo Simulation Toolkit® :


sz = state.getName().equals("up") ? 0.5 : -0.5;
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