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When I first learned about the four fundamental forces of nature, I assumed that they were just the only four kind of interactions there were. But after learning a little field theory, there are many other kinds of couplings, even in the standard model. So why isn't the Yukawa Higgs coupling considered a fifth fundamental force? To be a fundamental force, does there need to be a gauge boson mediating it?

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I think you're more or less right; what have been (sociologically) canonized as the fundamental forces (minus gravity) roughly correspond to the factors $U(1)$, $SU(2)$, and $SU(3)$ in the famous "$U(1)\times SU(2)\times SU(3)$" gauge symmetry of the standard model. But this is really a historical question, in my opinion. –  j.c. Nov 18 '10 at 18:40
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Uhm... how about: maybe because it wasn't observed yet? I think that is a pretty serious blow to anything trying to call itself fundamental :-) –  Marek Nov 18 '10 at 18:58
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Doesn't look like this has been mentioned yet: intuitively, forces are vectors and impart momentum, whereas the Higgs field is a scalar field that generates mass. If a fundamental interaction isn't mediated by a gauge boson, then it loses it's most force-like quality of being a vector field. –  David H Mar 28 '13 at 4:09
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5 Answers 5

The Higgs exchange between matter particles can certainly be called a force. Whether it can be viewed a fundamental force, is a matter of taste. But there is one important distinction between the force due to the Higgs exchange and the usual fundamental interactions. The strong and electroweak interactions are described as gauge interactions. It means that they are not put by hand but arise automatically when you require that the matter fields be invariant under local certain internal transformations (phase rotations, color transformations, etc.). In contrast to that, the "Higgs force" is put into the model by hand, as its presence is not driven by any symmetry consideration. You can equally nicely consider a model with zero Yukawa coupling.

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The catch here being that the symmetries themselves are "put into the model by hand." The Higgs coupling is driven by experimental results, and so while you could consider a model with no coupling, you'd have to explain spontaneous symmetry breaking some other way. Is your suggestion that some higher energy theory may in fact have some further symmetry that at low energy gives us the Higgs interaction, and that the higher level symmetry is the fundamental force, making the Higgs in some sense non-fundamental (like electric and magnetic separately) –  user542 Nov 18 '10 at 20:50
    
Concerning putting by hand, let's consider electromagnetism. You start from free field theory with complex field describing matter. Complex fields are put by hand, but after quantum mechanics this is not that unnatural. The lagrangian has the global U(1) invariance, so that the global phase is unobservable. This is rather expected. What you ask in addition is to make the phase unobservable locally. This also seems a rather reasonable requirement. That's it, the electromagnetic interactions follow. For non-abelian groups I agree that the initial global symmetry is put by hand. –  Igor Ivanov Nov 18 '10 at 21:34
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As for the second question, I just say that you can construct a theory with Higgs bosons but zero Yukawa couplings (no "direct Higgs force"), but you cannot construct a locally U(1) invariant theory without electromagnetic interactions. –  Igor Ivanov Nov 18 '10 at 21:38
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Forces and interactions are similar, so maybe for the purposes of this discussion we should define force as "interaction with a massless particle," as this gives the possibility of macroscopic-range "forces" (barring impeding effects such as confinement or symmetry breaking). After all, gravity is a massless but non-Yang-Mills force (mediated by spin-2, not spin-1, particle). There are some constraints on which spins (representations) of massless particles are possible in quantum field theory, but I'm not familiar enough to try to cite them off-hand, sorry.

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The Higgs field is not a vector field like, say, the vector potential of EM is. It arises from the observed coupling of massive particles to the weak field. So the Higgs boson is not a force-exchanging gauge boson in the same way as the other bosons of the Standard Model.

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The gravition wouldn't be a vectorial (it would have spin 2), but I would still be a force boson. Right? –  jinawee Nov 14 '13 at 16:12
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Scalar fields do transfer momentum in classical physics. Just take a look at acoustic signals in a gas. A strong sound can cause your windows to rattle. A well known example of energy transference by means of sound (pressure waves) is demonstrated with tuning forks. Quantum theory speaks of sound as particles (phonons), the discrete quanta of quantized mechanical vibrations of a christal lattice, whose longitudinal mode corresponds to our macroscopic perception of sound. In quantum field theory all fields need to be quantized in the end. If I've understood it correctly, the Higgs particle represents the discrete quanta of the quantized Higgs field. Since the Higgs field is a scalar field, its quanta are bosons. They carry kinetic energy, and this energy can be transmitted to all quantum fields that the Higgs field interacts with. You just need to take a look at the Lagrangian to see all the fields that the Higgs interacts with. Alternatively, look for the various Feynman diagrams that include Higgs lines. You can then easily see all the particles it interacts with.

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If gravity is a fundamental force, then the Higgs mechanism is also. This is is true whether they are related or not. The Higgs mechanism is certainly the source of the inertial mass that inspired Newton to quantify what a force is, and how it behaves.

Gravity, like the Higgs mechanism, can add mass/energy to matter in bulk (like constant acceleration), bend or even confine other force carrying bosons (photons) in space. This happens in the event horizon of black holes.

Not only is the Higgs mechanism a fundamental force, but the way it interacts is unquestionably unique among the fundamental forces. It slows down and limits the range of electroweak force carriers (W,Z) by breaking local symmetry, giving them mass without violating conservation of mass/energy.

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protected by Qmechanic Mar 3 at 0:49

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