I Number of Higgs "particles" per unit volume

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The number of Higgs "particles" per unit volume is not a meaningful quantity, as the Higgs field does not typically exist in a state with a defined particle number outside specific conditions like those in the LHC. The distinction between on-shell and off-shell Higgs bosons is crucial for understanding interactions. While the concept of particle number is problematic, questioning whether the Higgs field value remains constant in expanding space is valid. However, the Higgs field itself is an operator rather than a simple number, complicating discussions about its value. The average energy density of the Higgs field may remain constant as the universe expands, similar to dark energy density.
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Is the number of Higgs "particles" per unit volume constant?
Is the number of Higgs "particles" per unit volume constant (or Higgs field value), even in expanding space?
 
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mister i said:
the number of Higgs "particles" per unit volume
...is not even a meaningful quantity. The Higgs field is not even in a state with a meaningful "particle number" except in special cases like the interior of the LHC during an experimental run.
 
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PeterDonis said:
...is not even a meaningful quantity. The Higgs field is not even in a state with a meaningful "particle number" except in special cases like the interior of the LHC during an experimental run.
There is also a distinction between interactions with on-shell Higgs bosons v. interactions with off-shell Higgs bosons (i.e. virtual Higgs bosons).

But, while the particle part of the question is ill-posed, the question asking "Is the . . . Higgs field value [constant] . . ., even in expanding space?" Is not non-sensical on its face.
 
ohwilleke said:
the question asking "Is the . . . Higgs field value [constant] . . ., even in expanding space?" Is not non-sensical on its face.
Even the "Higgs field value" is problematic since a quantum field is not a number, it's an operator. But asking about something like the average energy density of the Higgs field would be reasonable. As far as I know that is constant as the universe expands, like dark energy density.
 
PeterDonis said:
...is not even a meaningful quantity.
Or it's zero pretty much everywhere.

Add "scare quotes" as necessary.
 
We often see discussions about what QM and QFT mean, but hardly anything on just how fundamental they are to much of physics. To rectify that, see the following; https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/66a6a6005101a2ffa86cdd48/original/a-derivation-of-maxwell-s-equations-from-first-principles.pdf 'Somewhat magically, if one then applies local gauge invariance to the Dirac Lagrangian, a field appears, and from this field it is possible to derive Maxwell’s...