Why does the existence of the Higgs Field require a Higgs Particle?

[imsmooth]

I believe I understand how the Higgs field imparts "mass" on a particle. Would someone explain how the existence of the Higgs Field means there has to be a Higgs Particle?

 

[Orodruin]

In the same way that the EM field implies the existence of a photon.

You have marked this thread "A", indicating that you have a graduate level understanding already. In that case, exactly which step in the quantisation of a scalar field do you find questionable?

 

[secur]

Any field in physics has an associated particle. For instance electron field, EM field (photons), sound field (phonons), W boson field. All these are linear and support wave solutions, therefore wave packet solutions. I.e., a so-called "particle". There's more to it, but that's the basic idea. There's nothing special about Higgs field in that regard although spin 0 makes the details a bit different.

 

[imsmooth]

I should have marked my understanding as "I".

Don't photons create their EM field? Isn't the EM field there because of the photons? So, if the Higgs is so rare because of its short existence, how does it create its field? It is probably my lack of understanding of if the particle creates the field or the existence of the particle implies a field exists.

 

[Nugatory]

I should have marked my understanding as "I".

Fixed it.

Don't photons create their EM field? Isn't the EM field there because of the photons?

It's the other way around. We have an EM field, and when we quantize it we discover that it supports quantized excitations that we call "photons". There's a pretty decent overview (but not even close to being a substitute for a real textbook) at:
http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

 

[haushofer]

I believe I understand how the Higgs field imparts "mass" on a particle. Would someone explain how the existence of the Higgs Field means there has to be a Higgs Particle?

It is a counting argument. The massive particles obtain their mass because they "eat" certain degrees of freedom of the Higgs field. At the end this leaves you with one remaining degree of freedom, which shows itself as a dynamical field on its own. After quantizing it, you get a particle from this, similar to how one obtains a photon from an EM-field.