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Ductaper
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in particle accelerators, we've seen the electromagnetic force and the weak force unified. How? Do W+, W-, Z, and photons dissappear, to be replaced by another fermion, or what?
This is one of those things that I hope to get cleared up. If I take for granted that there are these bosonic field quanta that account for beta decay and such, I still don't understand why they are emitted in the first place. Why is the electron "unhappy" about being an electron so much that it violates a natural principle? Is this one of those questions that is beyond the scope of physics? Is there any kind of mechanism that excites the electron so that it will emit a weak boson, or is the process completely random?zefram_c said:... the electron converted into a neutrino through emission of a W-.
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... they are constantly being emitted and reabsorbed.
I am familiar with the dispersion relation from relativity, but I don't understand quite what you were saying here about the W. What difference does it pick up (negative energy)?zefram_c said:... they obey the proper relativistic energy-momentum relation E2 = (pc)2+(mc2)2. The W does not. Since 4-momentum is conserved at the emission and absorption of the W, it can only pick up the difference and for certain it violates the above expression.
Let's do it.zefram_c said:It is quite difficult to explain the concept of mediators without resorting to quantum field theory, ...
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... if you want to work in the field ... you need to tackle the field theoretic ideas. (Of course, curiosity is encouraged, and if requested I can try to explain the QFT way of looking at things).
Check!zefram_c said:You will need a qualitative ... understanding of Lagrangian mechanics,
Check! (I think)zefram_c said:... and quite a bit of quantum mechanics.
I think I've seen this one before (someone tried to explain it to me on another forum).zefram_c said:There is a simple, and almost magical, way to derive all of the three interactions.
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I don't think I am quite appreciating this issue.zefram_c said:You then require that the Lagrangian have a symmetry known as local gauge invariance.
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I cannot give you a definite reason why we should demand that the local gauge symmetries hold; the fact is that this creates an extremely accurate and predictive theory. Also, local gauge theories are one of the few ways to write a self-consistent theory. If you try to write a 'naive' theory of the weak interaction with massive mediators W and Z without resorting to the gauge principle, the theory will contain nasty mathematical divergences that cannot be consistently removed.
Independently? That sounds absurd. Wouldn't that give you some crazy (or at least ill-defined) momentum behavior? (i.e. discontinuities)zefram_c said:This roughly means that you must be able to choose a different phase for the quantum field at each point in space.
So the Lagrangian of which you previously spoke is the "Dirac Lagrangian" (which could be acquired from the Dirac Hamiltonian)? I don't know much about the Dirac equation. That is where my formal QM instruction came to an end. I tried to read the chapter in Shankar about it (Ch 2#), but I couldn't follow his justifications (rather hand-wavy).zefram_c said:Now why would an electron be unhappy being an electron? In a simple Dirac field (ie obeying the free Dirac equation), it is perfectly happy
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But we just found that the Dirac Hamiltonian is incomplete: there are the new terms to consider.
I don't follow this at all.zefram_c said:Now every time a quantum is emitted or absorbed, a dimensionless constant is introduced.
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In a higher order calculation, the constant appears with increasingly large power.
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Now each of these orders gives you a magnitude. The *net* magnitude is obtained by adding all the magnitudes to each order.
This brings me to a new level of clarity. Excellent.zefram_c said:The electron emits a Z and recoils, the muon absorbs the Z and recoils. Both the electron and the muon are considered to be 'free' in their initial and final states, so they must surely obey the momentum-energy equation I posted. It follows that the 4-momentum of the Z is completely determined and it *cannot* obey the relation for a proper Z boson. But this is not a problem, as our theory dictates that there is no way to observe the virtual Z.
turin said:...
Independently? That sounds absurd. Wouldn't that give you some crazy (or at least ill-defined) momentum behavior? (i.e. discontinuities)
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To derive the Dirac equation we start with the Klein-Gordon equation.So the Lagrangian of which you previously spoke is the "Dirac Lagrangian" (which could be acquired from the Dirac Hamiltonian)? I don't know much about the Dirac equation. That is where my formal QM instruction came to an end. I tried to read the chapter in Shankar about it (Ch 2#), but I couldn't follow his justifications (rather hand-wavy).
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zefram_c said:Now every time a quantum is emitted or absorbed, a dimensionless constant is introduced.
turin said:I don't follow this at all
I don't think you can find any introductory book that includes neutrino oscillations yet... they were only confirmed a couple of years ago. But they are covered in courses.
But if you have little experience with the field, it's better to start with Griffiths since this one jumps straight into relativistic wave equations.
I hope that this is not absolute. My university offers no such course. You have all done a great job at explaining this crap so far. When I get the Griffiths text I will no doubt post a barrage of personal confusion that I trust y'all to mitigate.zefram_c said:... our posts cannot pretend to be a substitute for a formal course. If people become interested in the field as a result of our conversations, then a course that includes all the gory details is what they would benefit most from.
turin said:Why is the wavefunction a spinor? Is this emperical? I remember reading about some experiment that had a beam of electrons passing through a magnetic field. The beam split into discrete spots on the detecting screen. This is supposed to demonstrates the spinor nature of the electron's wave function. I don't quite follow how this demonstrates the spinor nature of the electron's wave function.
But my suggestion was well meaning. It's hard to keep motivated to work through ugly math when you don't understand the purpose behind it all, or at least I find it so. If someone were to ask me to work through a Feynman diagram without telling me why we do that, I don't know if I'd carry it through. In a course situation, things are different: students can get their hands dirty knowing there's the instructor to fall back on, to explain the how and the why. But our posts cannot pretend to be a substitute for a formal course. If people become interested in the field as a result of our conversations, then a course that includes all the gory details is what they would benefit most from.
The electroweak force is a fundamental force in physics that unifies the electromagnetic (EM) and weak forces into one unified theory. It is responsible for interactions between particles that have electric charge and weak isospin, such as electrons and quarks.
The electroweak force was discovered through a series of experiments in the 1960s and 1970s, including the discovery of the W and Z bosons at CERN in 1983. These experiments provided evidence for the unification of the EM and weak forces, leading to the development of the Standard Model of particle physics.
The electroweak force has several important implications in the field of particle physics. It helps explain the behavior of particles at high energies and is essential in understanding phenomena such as radioactive decay and the production of elements in the early universe. Additionally, the unification of the EM and weak forces has led to the development of other unified theories, such as the Grand Unified Theory.
The electromagnetic force is responsible for interactions between particles with electric charge, while the weak force is responsible for interactions between particles with weak isospin. The EM force is much stronger than the weak force, but it has an infinite range, while the weak force has a short range. The electroweak force unifies these two forces by showing that they are different manifestations of the same underlying force.
The electroweak force is one of the four fundamental forces in the Standard Model, along with the strong and gravitational forces. It is described by a mathematical theory called the electroweak theory, which combines the electromagnetic and weak forces into one unified force. The Standard Model has been incredibly successful in predicting the behavior of particles and has been confirmed by numerous experiments, including those at the Large Hadron Collider at CERN.