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SO(3)/SO(2)SO(3)/SO(2)

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Let G be a compact group. For a full spatial orientation one may choose SO(3) ; for a single direction carried by a spin-coherent state the parameter space is the sphere S2S^2 , equivalently the quotient SO(3)/SO(2) . That distinction is not cosmetic. A spin pointing along n\mathbf n does not encode rotation about n\mathbf n , so it cannot specify a full triad.

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SS

Symbol S

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OO

Symbol O

O is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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SO(3)/SO(2)SO(3)/SO(2)

Equation 11 · Evolutionary Physics

A Reference Frame Becomes Classical by Publishing Its Orientation

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Let G be a compact group. For a full spatial orientation one may choose SO(3) ; for a single direction carried by a spin-coherent state the parameter space is the sphere S2S^2 , equivalently the quotient SO(3)/SO(2) . That distinction is not cosmetic. A spin pointing along n\mathbf n does not encode rotation about n\mathbf n , so it cannot specify a full triad.

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