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:

When domain modelling with SysML, Generalization, inheritance, and even multiple inheritance are not "evil" and can be used relatively freely. We are not doing code-oriented Decorator patterns - an implementation choice - we are doing domain modelling!

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 S_z 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 Magic Cyber-Systems Engineer^® (Cameo Systems Modeler^®) or Magic Model Analyst^® (Cameo Simulation Toolkit^®) :


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

Up next

Neutrons and protons are spin-1/2 fermions and baryons

Notes

[ASSERTION]{STRONG} When domain modelling with SysML, Generalization, inheritance, and even multiple inheritance are not "evil" and can be used relatively freely. We are not doing code-oriented Decorator patterns - an implementation choice - we are doing domain modelling!

[POLICY, STYLE]{STRICT} Webel Parsing Analysis «pa» diagrams are NOT intended as final presentation diagrams! They serve merely to traceably elicit model elements, which may then be shown in other (typically much tidier) presentation diagrams elsewhere.

[ASSERTION]{STRICT} In Webel Parsing Analysis elicited model elements MUST eventually be moved out of the 'source' (or '0-source') Package/Model zone and under a main project Package/Model area. (Use the owner display option to check.)

[CAVEAT, ISSUE]{INFORMATIVE} The markup of Snippet page titles on this CMS web site is sometimes restricted (especially concerning subscripts and superscripts such as used in mathematical and scientific notation). Visit the linked Snippet page for the quote with full markup.

Snippets (quotes/extracts)

Leptons are spin 1/2 particles. The spin-statistics theorem thus implies that they are fermions and thus that they are subject to the Pauli exclusion principle: No two leptons of the same species can be in the same state at the same time.

Furthermore, it means that a lepton can have only two possible spin states, namely up or down.

there are only two possible values for a spin-1/2 particle: sz = +1/2 and sz = -1/2. These correspond to quantum states in which the spin component is pointing in the +z or −z directions respectively, and are often referred to as "spin up" and "spin down"

sz is the spin projection quantum number along the z-axis.

The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously.

In particle physics, a fermion is a particle that follows Fermi–Dirac statistics and generally has half odd integer spin 1/2, 3/2 etc. These particles obey the Pauli exclusion principle.

Some fermions are elementary particles, such as the electrons, and some are composite particles, such as the protons.

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The lepton Package Diagram so far

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