Equation 95 · No Particle Without a Cosigner
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Symbol D_rm det
m det is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
Nothing about 's definition requires flat spacetime; the response functional is written in terms of the Wightman function and proper time, both of which are perfectly well defined along a stationary worldline in a curved, static exterior. What changes in curved spacetime is that the field state is no longer unique even after the geometry is fixed: a Schwarzschild exterior supports the Boulware vacuum (empty at infinity, singular at the horizon), the Hartle-Hawking state (thermal everywhere, matching a black hole in equilibrium with its own radiation), and the Unruh state (matching outgoing Hawking flux with no incoming radiation), and a detector’s response depends on which of the…
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Nothing about 's definition requires flat spacetime; the response functional is written in terms of the Wightman function and proper time, both of which are perfectly well defined along a stationary worldline in a curved, static exterior. What changes in curved spacetime is that the field state is no longer unique even after the geometry is fixed: a Schwarzschild exterior supports the Boulware vacuum (empty at infinity, singular at the horizon), the Hartle-Hawking state (thermal everywhere, matching a black hole in equilibrium with its own radiation), and the Unruh state (matching outgoing Hawking flux with no incoming radiation), and a detector’s response depends on which of the three it is placed in — reinforcing, rather than complicating, the first treaty clause.
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