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I have done a bunch of research regarding the Higgs field and Higgs boson but I keep running into issues when trying to understand how the interactions between the Higgs field and fermions occur. I understand that it is due to Yukawa interactions but this seems to be purely mathematical and doesn’t help me understand how the particles gain mass, other than this I have found 4 different answers that I can’t seem to link.

The first is from pbs space time and a CERN bulletin page that implies that the weak hypercharge is constantly exchanged between particles and the Higgs field which constantly flipping it chirality and therefore causing it to evolve meaning it has mass.

The other implies that Higgs bosons transferred between the field of the fermion and the Higgs field which some how provides energy that manifests as mass. But I thought Higgs bosons didn’t take part in giving mass to these particles.

Another states that the particles continue to move at the speed of light but bounce off the Higgs field which makes them appear to move slower and so they must have mass.

The final is from multiple apparently inaccurate analogies that imply there is a drag on the particle from the Higgs field which causes the mass. On the other hand I see that they don’t slow down and only gain inertia so this is incorrect, but how would they continue moving at light speed if they gain a mass.

Are any of these correct or incorrect, or maybe I’ve misunderstood something?. If not what actually mediates the interactions because the sudden transfer of energy without any carrier doesn’t make sense to me. Apologies if this has been asked before, pls send the link if so.

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    $\begingroup$ Those explanations are only intended to provide some intuition by using analogies from more familiar classical physics, so they are inherently limited since the underlying theory is fundamentally not classical. If you want to gain a better and more accurate understanding, I doubt if there is a way that avoids studying the math. $\endgroup$
    – J. Delaney
    Commented Jun 17, 2023 at 9:00
  • $\begingroup$ @J.Delaney from the maths I think I can understand the changes to the system but when it comes to the method I’m still very much in the dark. As far as I’m aware the langrangian and the implementation of the Higgs field causes the mass to work in the equation due to the spontaneous symmetry breaking that causes the non-zero vev of the Higgs field. And I think it is energy in the elementary particles that comes from this field that manifest as the mass, which is represented by an increase in inertia. But I fail to see from the math and how the interactions occur physically. $\endgroup$
    – Random34544
    Commented Jun 17, 2023 at 14:19
  • $\begingroup$ Essentially is it a force, a carrier, virtual particles or what that causes the interactions. I’m really new to this so I’m sure it’s me. Maybe the question I’m asking is just not currently known in the science community? $\endgroup$
    – Random34544
    Commented Jun 17, 2023 at 14:21
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    $\begingroup$ Your 3rd and 4th explanations are bogus and collateral damage of irresponsible science reporting, and not worth thinking about, especially as some type of energy transfers to "formerly" massless particles. The 1st and 2nd overlap some type of shared metaphor, but the rule is "you start from the math, and Then you summarize it through metaphors", if you are so inclined. In this specific case, the metaphors confuse you and drive you away from the sound math in search of an elusive "physically". Galileo said: "The book of nature is written in math". $\endgroup$
    – Cosmas Zachos
    Commented Jun 17, 2023 at 16:28
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    $\begingroup$ @CosmasZachos That is only partially true. The real problem here doesn't lie with the math or lack thereof. It's solely based in the fact that we do not have analogous experiences to quantum fields. We can describe them all we want (with or without math), but since nothing in our direct environment behaves even remotely like a quantum field we have absolutely no "handles" on them. Quite literally. The closest one can get are probably two magnets attracting and repelling each other... for a classical approximation. $\endgroup$
    – FlatterMann
    Commented Jun 17, 2023 at 19:45

2 Answers 2

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What are the actual interactions between the Higgs field and fermions

All the particles in the table of the standard model are represented by a field. The field mathematically is represented by the plane wave solution of the corresponding particle, Dirac for fermions, Klein Gordon for bosons, and covers all space time. The electron field covers all space time the same is true as well for all particle fields in the table, including the Higgs.

The Higgs mechanism is not an interaction, it is a mathematical way to break the symmetry of the zero masses before the symmetry breaking time.

The only connection the Higgs field has with the fermion particles, in the main stream physics theories of today, happened once, in cosmological times, when elementary particles from massless became massive at the symmetry breaking time of weak interactions.

In the big bang model for example

enter image description here

Fields do not interact in quantum field theory, fields are acted upon by creation and annihilation operators which manifest interactions between particles.

Energy exchanges happen between particles , not between fields.

As the Higgs field is necessary in order to model mathematically the symmetry breaking point in time, quantum field theory demands that a Higgs particle should exist .This particle was searched for and found at the LHC.

The Higgs field acted upon by a creation operator will describe the Higgs boson interaction with particles or the decay of the Higgs boson. decay , not the Higgs field.

In general the energy is input coming with the four vectors of the particles , the fields do not have a four vector describing them, just a quantum mechanical wavefunction.

The popularized dragging analogies are misleading and incorrect as far as the actual mathematics of the mechanism.

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  • $\begingroup$ So when you say the only connection was at the Big Bang how come they continue to interact with the Higgs field. How did this massless to massive interaction actually occur is my main question. If energy exchanges don’t occur between fields then how did the Higgs field impart mass without exchanging energy. Sorry for the confusion and thx for your time $\endgroup$
    – Random34544
    Commented Jun 17, 2023 at 14:33
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    $\begingroup$ @Random34544 It is not an interaction, it is a mechanism, it is interaction in the general everyday meaning of interaction. $\endgroup$
    – anna v
    Commented Jun 17, 2023 at 19:41
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    $\begingroup$ @Random34544 What anna_v is trying to tell you is that you are trying to explain the behavior of ice through the behavior of molecules in steam. Of course it won't work. Ice behaves differently from steam, even though the molecular interactions are "the same". That simply doesn't help much because what matters are the effective interactions after the phase transition. The standard model is like ice... it's a frozen remnant of an earlier, much hotter state of the universe. That is the reason why it seems "so complicated". $\endgroup$
    – FlatterMann
    Commented Jun 17, 2023 at 19:49
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    $\begingroup$ @FlatterMann thanks. that is a good analogy. $\endgroup$
    – anna v
    Commented Jun 18, 2023 at 5:55
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I understand the higgs field as the average of the electromagnetic spectrum at rest from which the big bang created noise, subsequent thought & the electromagnetic signal of intent (phi?=psi?).

Would this resolve the issue around the differential manifold? https://en.wikipedia.org/wiki/Talk:Differentiable_manifold

I think of it as the evolution of chaos from silence into (structured?=unstructured?) harmony of noise at different frequencies, such that the higgs, ("elevates" or negates Magnitude) across the complex manifold of the electromagnetic spectrum to measurably cross atlas through oscillating magnitude wells. I don't know where these or Intent came from, I just know, like any one other of you, I too exist and emergent in the manifold. It seems we all materialized out of the emergence of these rules over time such that the point in a line is finite in a cycled graph among the silenced root of the spectrum across complex manifolds since the range of fields dictate non Euclidean lines across temporal hyperspace.

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    $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
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    Commented Apr 21 at 21:59
  • $\begingroup$ Added context for clarity. $\endgroup$
    – John Gomez
    Commented Apr 21 at 22:05

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