Symbol K_i
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The structure is the same one that makes an Aharonov–Bohm phase or a Berry-phase holonomy nonzero: a closed path in a classical parameter space picks up a phase set by a curvature that lives on that space, even though nothing classical distinguishes the endpoint from the start. Here the “curvature” is the commutator [,] itself, and the “charge” that couples to it is mass. The analogy is a guide to intuition, not a claim of identity — there is no background field on the group manifold in the electromagnetic sense, only the algebra’s own structure constants — but it explains why the effect survives however the loop’s interior path is traced, so long as the net translation and net boost…
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Symbol P_j
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Equation 39 · Evolutionary Physics
The Clock That Comes Back Wrong by Exactly Its Mass
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
The structure is the same one that makes an Aharonov–Bohm phase or a Berry-phase holonomy nonzero: a closed path in a classical parameter space picks up a phase set by a curvature that lives on that space, even though nothing classical distinguishes the endpoint from the start. Here the “curvature” is the commutator [,] itself, and the “charge” that couples to it is mass. The analogy is a guide to intuition, not a claim of identity — there is no background field on the group manifold in the electromagnetic sense, only the algebra’s own structure constants — but it explains why the effect survives however the loop’s interior path is traced, so long as the net translation and net boost…
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