[tutfbhuf]

An example of a group homomorphism in physics is the relationship between the rotational symmetry group of a physical system (often the group SO(3) for three-dimensional rotations or SU(2) for spin systems) and the representation of that group by the angular momentum operators in quantum mechanics. The angular momentum operators in quantum mechanics form a representation of the symmetry group because they satisfy the same commutation relations as the infinitesimal generators of the group. This means that the algebraic structure of the rotational symmetry group is mirrored by the algebraic structure of the angular momentum operators, and the way these operators transform states in the Hilbert space of the quantum system reflects the symmetry properties of the system.

[613style]

I'm not sure if you intend this as a helpful analogy for an undergrad or as an argument in favor of groups/homomorphisms being created to match reality, but I don't think it applies very well to either.

(Though it is very interesting!)