This is my first comment. I am not a physicist or mathematician, but I am interested in finding out more. I've recently read that the Higgs Boson gives itself mass, this is probably a painful over simplification to experts in the field but it's what I can get my head around thus far. I am trying to understand the mechanism behind this self interaction. What triggered the first instance of that interaction in the Higgs field? Again, I'm not sure if I'm evening asking the right question and need a gentle steer.
Indeed Higgs mechanism is, at first, hard to understand, even for people with baggage in physics. I will try my best to make it understandable.
Our current theory of the universe at subatomic scales goes trhough Quantum Field Theory (QFT). With this model the universe is though as filled with differents field: one field for electrons, one for up-quarks, and so on. Every particle is an excitation of its corresponding field.
The Standard Model of Particles predicted that some particles, like the bosons carrying the weak interaction should have zero-mass, however they are incredibly heavy. Peter Higgs, in analogy of an effect descirbed in condesed matter, proposed that together with quarks, leptons and carriers of force, must exist another field (the Higgs field) that provides mass to those bosons via interactions with those. A helpfull analogy: consider the mass as the effort you need to move an object. Moving it through vacumm requires no effort, so it has no mass. However if the space is filled with water (representing the Higgs field) the object will be much mor complicated to move and, hence, more massive.
A straightforward generalisation of this effect is that the Higgs boson couples no only with weak bosons, but will all the particles. So all the (fundamental) have a mass proportional to the stregth of the coupling with the Higgs field.
While doing the maths, one see that the simples field we can accept is a scalar field with no electrical charge. Once one calculate the dinamycs of the field, there are three terms that arises in the equations: - A term proportional to $H^2$ which gives the mass of the field - A term proportional to $H^3$ and a term proportional to $H^4$ which gives interactions between the Higgs field with itself.
All of those can be seen as interactions between Higgs particles
The main problem with this representation is that lead to the confusion thet interactions between fields, go linearly in time, i.e. that in order to obtain mass, a particle must interact with the Higgs field first. However in Quantum Field Theory, the concept of time is always dificult to understand. QFT is a covariant theory: must give the same results independently of the observer. Since two observers can have different notions of time, (see Relativity of simultaneity for example) the notion of "before" an "after" is not always clear.
The image one should take in mind while studying particle interactions is that all the interactions happen at the same time. The Higgs field does not need to interact with the Higgs boson to aquire mass, but because it is always interacting with itself, it shows mass. Nothing "trigger" a first interaction which lead to the dynamics of the field.
(Note: In a poetical sense, maybe this first evet could have be considered the Big Bang, which, in the big picture is the origin of every interaction. However probably is not the answer you are looking for and the Standard Model is not sure to be applicable in the first instants of the universe.)
The Higgs Mechanism
Until 2012, people actually laughed at Peter Higgs' idea of energy creating matter on a whole different plate than the rest of physics. But on July 4, 2012, the CERN LHC discovered evidence of the Higgs Boson, the exchange particle in the ordeal and Higgs was awarded the Nobel Prize. This proves that in physics, an insane idea that makes utterly no sense and that the rest of the population denounces can be the most brilliant theory ever discovered (another example of this is Relativity).
Scene: The Big Bang goes off, just pure energy, no fermions. In less than a sextillionth of a second, the elementary particles are formed and the universe becomes a super dense fog, trapping all of the photons for the
300,000 years. The formation of these particles is key. As explained under Energy-Mass, most of the energy in baryons actually comes from the energy in the gluons. The quarks themselves account for less than 1% of the total mass. This is called intrinsic mass and it too comes from energy. This property originates in the depths of quantum field theory, a phenomenon in which everything belongs to its coordinated field, the gluon in the gluon field, the photon in the photon field, the quark in the quark field and so on. These fields are kind of like maps. Take the photon field for example. Imagine that everything in the universe has a certain photonic quality. In absolute darkness, this is usually pretty close to 0. There was a problem here. When you add energy to a field, it vibrates. That vibration creates the photon. Everything, gluons, quarks, electrons, is just an energetic vibration on its field. There's more, these field vibrations all interact with one another by exchanging energy. 1950s Quantum Field Theory gives an accurate description of electrons, but it explains that it has no mass and thereby would not experience time. However, we know for a fact that electrons add weight to atoms and experience time. You see, the electron, like most leptons, has a two-way spin, switching at a steady pace between "left-handed" and "right-handed." Since it does this chronologically, it has to experience time. This is where the Higgs mechanism becomes involved. The universe does not like you if you're left handed. Now I realize I'm insulting 10% of the global population, but it's true, the universe cares so much that to be left handed you have to possess a certain particle. Before I go any further, let's take a look at gravitons. They are definitely massless and do not experience time, they never stop and move straight through atoms, not once switching "hands." Meanwhile, the electron is constantly being blocked, by nuclei, electrons, or any random fermion that happens to be in their way. Why do the graviton and electron behave so differently if they're both vibrations in their quantum fields? There has to be a property that blocks the electron that doesn't apply to gravitons or photons. This is where the spin comes in. The certain particle that allows electrons to switch "hands" is called weak hypercharge. While non-ambidextrous particles can fly through space without any form of impediment, the weak hypercharge forces "left-handed" electrons to interact with the weak force along with the electromagnetic force which happens to be the makeup of the electroweak force. Coincidence? I think not. Anyway, to switch between these forces electrons have to be able to shake or find a weak hypercharge (depending on their spin). So where can I find a weak hypercharge? On the Higgs field. Unlike the other fields which, in empty space, stay around 0, the Higgs field has a positive charge, attracting electrons. Another thing that makes the Higgs field stick out is its everything-ness. While other fields only have one of their particle per energetic vibration, the Higgs field has an infinite number of weak hypercharges everywhere. As the electron passes through space, it is attacked by weak hypercharges, trying
to attract or break away from the electron causing it switch "hands." The more energy on the Higgs field, the faster the weak hypercharges sink and break away. Thus, the electron cannot get through the Higgs field and is forced to feel mass and therefore live for an infinite amount time.
Though due to gluons and their natural attraction to one another, quarks would not be capable of moving the speed of light anyway, they too experience the mark of the Higgs field. Quarks do not need weak hypercharge, but that is actually just a side effect of the Higgs field, the real purpose is to provide a slower/stopper for particles like electrons, that should be moving the speed of light. The real question here is not "what does" but "what doesn't." There are two particles that do not (in rest) interact with the Higgs field. They are the graviton and the photon.
Gravitons do not interact with anything in the first place. They simply travel through space carrying gravitational waves. There is an extremely dense mathematical explanation for this, but physics is supposed to be fun, right? Photons, on the other hand, do interact with matter, but not other fields. Unlike most particles, photons only give energy to other photons, therefore they do not interact with the Higgs field. Again, a dense mathematical explanation - for your professor to explain.
But what carries the Higgs field and its collection of weak hypercharge anyway? Enter: Higgs Boson. Like for other fields, the Higgs boson (AKA God particle) is created by the energetic vibration of the Higgs field. It is literally the exchange particle of mass. The Higgs is also probably the most expensive particle. It took over $13 billion to find this particle at the LHC, but when it was done, the standard model was finished (at least for matter). Though the Higgs boson has a mere half-life of 10-22 seconds, it proves critical to all of physics.