Symbol F_x
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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where W is the field’s two-point Wightman function evaluated along the trajectory [ 5 ] . Three things in this expression are worth fixing in the reader’s mind before anything else happens to it. First, is proper time — the detector’s own clock, the only time variable with unambiguous physical meaning for a single worldline — never the coordinate time of whatever chart the trajectory happens to be written in. Second, is conjugate to that same proper time; it is an energy gap measured in the detector’s own instantaneous rest frame, not a coordinate-frame frequency. Third, the field state enters only through W , and changing the field state — the ordinary vacuum, a thermal state,…
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Equation 15 · Evolutionary Physics
No Particle Without a Cosigner
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
where W is the field’s two-point Wightman function evaluated along the trajectory [ 5 ] . Three things in this expression are worth fixing in the reader’s mind before anything else happens to it. First, is proper time — the detector’s own clock, the only time variable with unambiguous physical meaning for a single worldline — never the coordinate time of whatever chart the trajectory happens to be written in. Second, is conjugate to that same proper time; it is an energy gap measured in the detector’s own instantaneous rest frame, not a coordinate-frame frequency. Third, the field state enters only through W , and changing the field state — the ordinary vacuum, a thermal state,…
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