The Higgs particle and field.

[geordief]

Suppose we have a massive particle (Would a proton be the smallest or can quarks exist as an individual massive particle?) moving in the Higgs Field.

 

Does its trajectory change if it gets close to an  actual Higgs  particle as opposed to the Field?

 

I have a picture of a Higgs particle  acting like a source of gravitation  of the particle but doubtless this is both simplistic and wrong.

 

Also wondering how massless particles' trajectories are affected...

 

 

 

[joigus]

47 minutes ago, geordief said:

Would a proton be the smallest or can quarks exist as an individual massive particle?

It's not either/or. Quarks cannot exist as individual massive particles, and protons aren't the smallest hadrons (strong interactive particles). Mesons are short-lived but real enough, and are composites of quark-antiquark. And they are smaller than protons.

The so-called Higgs multiplet is actually a quantum field with 4 degrees of freedom. 3 of them are called Goldstone bosons and they're the ones that massless particles swallow up in order to acquire mass. The left over degree of freedom is what we call the Higgs boson.

So trying to picture what happens in terms of an actual "swarm of Higgs particles" flying around is the wrong way to picture it.

This leftover DOF of the Higgs multiplet is normally unoccupied. Occupation number = 0, in the QFT parlance. So it's not really there. You have to actually provide a lot of energy to make it show up. The swallowed up DOFs are what's dragging the massless particles to make them look as they've got mass.

I don't know whether that answers your question, if only to clarify that the actual picture is a bit more sofisticated than particles modifying other particle's trajectories.

Did that help at all?

1 hour ago, geordief said:

I have a picture of a Higgs particle  acting like a source of gravitation  of the particle but doubtless this is both simplistic and wrong.

It's all energy that's the source of gravity, not only mass, and certainly not just the Higgs field.

[geordief]

1 minute ago, joigus said:

It's not either/or. Quarks cannot exist as individual massive particles, and protons aren't the smallest hadrons (strong interactive particles). Mesons are short-lived but real enough, and are composites of quark-antiquark. And they are smaller than protons.

The so-called Higgs multiplet is actually a quantum field with 4 degrees of freedom. 3 of them are called Goldstone bosons and they're the ones that massless particles swallow up in order to acquire mass. The left over degree of freedom is what we call the Higgs boson.

So trying to picture what happens in terms of an actual "swarm of Higgs particles" flying around is the wrong way to picture it.

This leftover DOF of the Higgs multiplet is normally unoccupied. Occupation number = 0, in the QFT parlance. So it's not really there. You have to actually provide a lot of energy to make it show up. The swallowed up DOFs are what's dragging the massless particles to make them look as they've got mass.

I don't know whether that answers your question, if only to clarify that the actual picture is a bit more sofisticated than particles modifying other particle's trajectories.

Did that help at all?

Thanks.Of course it helps  but I  need  much more time to try to learn and digest some of  that and to reassess what my questions about it might be  (or maybe post a different thread  on a different but related  subject at some stage) 

[joigus]

1 minute ago, geordief said:

Thanks.Of course it helps  but I  need  much more time to try to learn and digest some of  that and to reassess what my questions about it might be  (or maybe post a different thread  on a different but related  subject at some stage) 

No problem. You must think of quantum fields as things of which it makes sense to think of them as "being there" but in a vacant state. The field people usually refer to is the vacuum of the Higgs field. One has to spend considerable amount of energy (and money) to take it to an excited state with occupation number = 1.

[geordief]

21 minutes ago, joigus said:

No problem. You must think of quantum fields as things of which it makes sense to think of them as "being there" but in a vacant state. The field people usually refer to is the vacuum of the Higgs field. One has to spend considerable amount of energy (and money) to take it to an excited state with occupation number = 1.

And yet ,apparently we would not have gravitational fields (are they quantum fields or classical fields? Classical ,I imagine.) without the effect of the Higgs Field.

 

So does that mean it has been activated for all the objects subject to the Gravitational Field? 

[joigus]

2 minutes ago, geordief said:

And yet ,apparently we would not have gravitational fields (are they quantum fields or classical fields? Classical ,I imagine.) without the effect of the Higgs Field.

Why? A world made of photons would gravitate.

It's energy that's the source of gravitation, not mass.

All fields are quantum fields. They should be. It's just that people haven't been able to make sense of quantum gravitational fields so far.

[MigL]

Simplest way to think of the Higgs mechanism is as a 'scalar' field.
Unlike vector, or tensor, fields the value at each point in space has no direction assigned to it, so nothing will be 'forced' in any particular direction.

[Mordred]

In this sense I like Sean Carolls descriptive he once gave in a lecture.

If you want a Higgs boson you need to poke it.

As Mentioned by Joigus the Higgs scalar field is a scalar field in order to get A Higgs boson out of it you need sufficient localized  energy. The difference between scalar fields vs other fields such as vector, spinor and tensor fields is well described by Migl.

One thing that Joigus correctly noted the Higgs field has 4 effective degrees of freedom making this scalar field a complex doublet.

 

Edited June 29 by Mordred

[studiot]

Here are two quotes from the book I recently mentioned in the book talk section that aptly illustrate how readily Frank Close gets to the nub if the matter.

 

[geordief]

1 hour ago, joigus said:

It's energy that's the source of gravitation, not mass

So the effect on gravitation from the Higgs field is "derivative" and not fundamental?

It affects the way some things cause gravitation but not others (eg photons) which have gravitation "built in " (but less obviously)?

Mass is not the same as energy  but can be converted to it ? (is it a two way street?)

7 minutes ago, studiot said:

Here are two quotes from the book I recently mentioned in the book talk section that aptly illustrate how readily Frank Close gets to the nub if the matter.

 

Thanks. Very interesting

[Mordred]

2 minutes ago, geordief said:

So the effect on gravitation from the Higgs field is "derivative" and not fundamental?

It affects the way some things cause gravitation but not others (eg photons) which have gravitation "built in " (but less obviously)?

Mass is not the same as energy  but can be converted to it ? (is it a two way street?)

No that description doesn't work. When particles acquire the mass term they then contribute to the energy momentum tensor which in turn gives rise to curvature. A non interacting Higgs field doesn't contribute to the energy momentum terms for curvature. 

When particles acquire mass there is a mixing angle involved ( mathematical mixing angles ) not space/spacetime mixing angles.

\(A_\mu\) an \(Z_\mu\)

\[W^3_\mu=Z_\mu cos\theta_W+A_\mu sin\theta_W\]

\[B_\mu= Z_\mu sin\theta_W+A_\mu cos\theta_W\]

\[Z_\mu=W^3_\mu cos\theta_W+B_\mu sin\theta_W\]

These are the mixing angles. After electroweak symmetry these mixings gives rise to the Mexican hat potential to the Higgs VeV (vacuum expectation value.) The left over degree of freedom due to no mixing angle for photons is what gives rise to the Higgs field VeV value today.

However that left over doesn't contribute to curvature. ( in point of detail assuming Higgs as Cosmological constant is correct) then it's value would act as the cosmological constant term.

 

[geordief]

6 minutes ago, Mordred said:

No that description doesn't work. When particles acquire the mass term they then contribute to the energy momentum tensor which in turn gives rise to curvature. A non interacting Higgs field doesn't contribute to the energy momentum terms for curvature. 

When particles acquire mass there is a mixing angle involved ( mathematical mixing angles ) not space/spacetime mixing angles.

Aμ an Zμ

 

W3μ=ZμcosθW+AμsinθW

 

 

Bμ=ZμsinθW+AμcosθW

 

 

Zμ=W3μcosθW+BμsinθW

 

These are the mixing angles. After electroweak symmetry these mixings gives rise to the Mexican hat potential to the Higgs VeV (vacuum expectation value.) The left over degree of freedom due to no mixing angle for photons is what gives rise to the Higgs field VeV value today.

However that left over doesn't contribute to curvature. ( in point of detail assuming Higgs as Cosmological constant is correct) then it's value would act as the cosmological constant term.

 

Thanks.I will bow out now as I  don't even have a  sketchy outline of this subject.

[Mordred]

No you had some good ideas it's simply the scalar field only contributes to the T_(00) component of the stress tensor which describes the energy density but doesn't give rise to curvature.

So your questions were good ones.

The curvature terms are described using the particles that have acquired mass (though massless particles can contribute) but not the Higgs field itself. That's an important distinction. 

Edited June 29 by Mordred

[joigus]

On 6/29/2024 at 5:19 PM, geordief said:

So the effect on gravitation from the Higgs field is "derivative" and not fundamental?

Mass really is rest energy. That's all it is. You have to think of mass as some kind of cohesion energy. Mass is the energy that a piece of matter still has even if you take it to a standstill. (To understand this you need Einstein's theory of special relativity).

A world with no mass is conceivable. It would look the same at every length scale. A world with no energy is nearly unconceivable, OTOH.

I agree with @Mordred that those are not necessarily bad questions. They're good --if hard-- questions.

Mixing --that Mordred mentioned-- further complicates things: Particles with well defined mass don't have other quantum numbers that well defined. They are quantum superpositions of states with different quantum numbers (analogues of electric charge). Some particles are so-and-so percent of this particle and so-and-so percent of that other particle. And this "mixing angles" (that determine how much of this and how much of that there is) are fixed that way since the beginning[?] of the universe... It's very confusing. My advice would be: Don't think about mixing for the time being.

In QFT, mass is a mess. In Newton's mechanics, it's simple because it's a primitive concept and doesn't have to be justified.

(Sorry I wrote "sofisticated" instead of "sophisticated". I'm bilingual, and I get the spelling of Latin/Greek-root words wrong when I'm writing in a hurry.)