$$\rho_R(g)=U_R(g)\rho_R(e)U_R(g)^\dagger$$

Equation 17 · Evolutionary Physics

A Reference Frame Becomes Classical by Publishing Its Orientation

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Choose a declared laboratory frame L only as a temporary coordinate system. Let $g_{RL}$ be the rotor’s orientation relative to L . A covariant family of rotor states can be written $\rho_R(g)=U_R(g)\rho_R(e)U_R(g)^\dagger$. This is a definition. e is the identity orientation, $U_R$ is a unitary representation of G , and $\rho_R(e)$ is the chosen fiducial state. Nothing in the equation makes g absolute. Changing the reference frame by h changes the coordinate label and representation together.

Meanings in this article

• $\rho_R$: the chosen fiducial state.
• $U_R$: a unitary representation of G.
• $e$: the identity orientation.

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