Dietterich Labs
Maxwell Lagrangian Derivation | Covariant Electromagnetism | Electrodynamics
updated
Note: They were sitting in water only briefly just after watering. None of my nepenthes have ever had root problems.
Clarification: By uncoupled, I don't just mean that there is no term in which k_z and m multiply each other. I am also referring to the fact that they multiply different alpha matrices. The relations satisfied by the alpha matrices ensure that cross terms don't show up. In this video, I only remembered to mention this at the very end.
That Cartesian video:
youtu.be/M9w2Plj7brw
The ladder operator video:
youtu.be/aDAw3glRHDw
My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
Clarification: By uncoupled, I don't just mean that there is no term in which k_z and m multiply each other. I am also referring to the fact that they multiply different alpha matrices. The relations satisfied by the alpha matrices ensure that cross terms don't show up.
That previous video I was talking about:
youtu.be/aDAw3glRHDw
The Schrodinger video I was talking about:
youtu.be/nPMde3zBgNo
My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
That previous video I was talking about:
youtu.be/nPMde3zBgNo
My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
Typo: At 5:43, it should be Y(l , m+½) = (Sqrt { [ ( 2l + 1 ) ÷ 4π ] ⋅ ( l − m − ½ )! ÷ ( l + m + ½ )! } )⋅[exp i(m+½)φ]⋅P(l , m+½)
Here is my previous video on Bhabha scattering:
youtu.be/iXgpsPYZ7hg
Note: the bosonic normalization I chose to use in the general differential scattering cross section is not arbitrary, apart from not including mass factors. It is the one consistent with the usual spinor-helicity formalism.
Part 1:
youtu.be/ljKh36Em87s
Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
Clarification: I ignored the negative root because it would not lead to a smooth trial function, and would therefore be much worse than the simple square guess that we were trying to improve on. Also, one in general has to check that the root one does select actually is a minimum, a step that I skipped here.
To be clear: when I say "less reputable suppliers", I mean from a seed viability perspective, not from a plant poaching perspective. I do not support plant poaching, and do not buy poached plants.
My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
The link to my non-degenerate perturbation theory video:
youtu.be/ZjUj7GHU2UM
My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
Typo at 2:25: On the RHS of the first equation of motion, there should be a square on the theta-dot.
My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
Note: It appears that I forgot to explicitly enter q=0 in the first selection rule, in the second line after the Wigner-Eckart theorem.
My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
I suppose I should have draws the 2s orbital bigger.
Accelerating pendulum cart video:
youtu.be/lEgkCbFIHtI
Harmonic oscillator pendulum cart video:
youtu.be/tHHLKUAMdgI
My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
Typo: In my initial expression for y_1, the angle should be theta_1.
Note: A good point was made in the comments section of this video. What I called an eigenvalue problem isn't exactly that, because neither V-tilde of T-tilde are the identity. One could take the base matrix equation, and multiply it by T-tilde-inverse to convert it into one, but that doesn't change how the system is actually solved. I therefore kept calling it an eigenvalue problem without fully converting it into one.
My Quantum Mechanics Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsAFCzO-YWGlJ4TNv8sMdy
My Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
Making this video was a bigger job than any I had made yet, so if you know anyone who would like it, please don't hesitate to share it with them.
There is a typo in this video at 49:31. I meant to write and say "and h_γδ describes a massive analogue of a graviton (the traceless part of h_γδ) and a massive scalar (the trace of h_γδ)." The massless case shows up in the closed string.
The rest of my quantum field theory lecture series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
The laser is a 40 watt carbon dioxide tube laser.
It is a basic 40 watt CO2 tube laser.
My video on the complete QEW Lagrangian (my last mathematical physics video):
youtu.be/mnArKhQNsck
My video on the QCD lagrangian:
youtu.be/jeKgZmkxlzo
My Quantum Field Theory Video Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
Minor Typo:
In the unbroken QEW and standard model Lagrangian densities, the subscript “l” on the left hand factor in the last quark Yukawa coupling term is supposed to be a subscript “q.” The same issue shows up in the attached tables of definitions for “L-tilde_q”. Hopefully these fairly obvious typos don't confuse people too much.
My last video on spontaneous symmetry breaking in QEW, where I introduce QEW theory for one generation of leptons:
youtu.be/A4hRN5Gqjcs
Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
Minor Typo:
In the complete unbroken QEW Lagrangian density, the subscript “l” on the left hand factor in the last quark Yukawa coupling term is supposed to be a subscript “q.” The same issue shows up in the attached table of definitions for “L-tilde_q”. Hopefully these fairly obvious typos doesn’t confuse people too much.
Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
There are a few places in this video where I wrote out the finished charged current lagrangian without using the psi notation that I broadly adopted for Dirac fermion fields. The way I accidentally wrote it is a common alternative notation, and the context still makes everything clear, so it shouldn't be a big problem, but I still wanted to clarify.
Also, the subscript "SM" on the last two Lagrangians is supposed to be "WSM" standing for Weinberg-Salam Model.
When I state the gauge transformation laws, "R" refers to the right handed sector, which consists only of e_R. I meant to just write e_R, but I accidentally mixed in an alternative notation again.
Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
It's worth pointing out that I chose to leave the vector boson interactions inside the field strength tensor terms, to keep the result compact. This does mean that the Proca Lagrangian density doesn't appear explicitly in the final answer, although it is clearly present. It also means that the massless and massive vector boson Lagrangians do contain fields of the other type via the still-implicit vector boson interaction terms. Because it is clear where all the important parts are, I decided that this would be a good compromise between clarity and compactness.
That Spontaneous Symmetry Breaking Video I mentioned:
youtu.be/MYBi4sgP4t8
Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
At 4:28 there is a minor typo. In the very bottom right most equation, there is an A_mu on the left side of the equals sign that clearly isn't supposed to be there.
Quantum Field Theory Lecture Series:
https://www.youtube.com/playlist?list...
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
It's worth pointing out that I chose to leave the vector boson interactions inside the field strength tensor terms, to keep the result compact. This does mean that the Proca Lagrangian density doesn't appear explicitly in the final answer, although it is clearly present. It also means that the massless and massive vector boson Lagrangians do contain fields of the other type via the still-implicit vector boson interaction terms. Because it is clear where all the important parts are, I decided that this would be a good compromise between clarity and compactness.
My last video on spontaneous symmetry breaking:
youtu.be/MYBi4sgP4t8
Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
It's worth pointing out that I chose to leave the vector boson interactions inside the field strength tensor terms, to keep the result compact. This does mean that the Proca Lagrangian density doesn't appear explicitly in the final answer, although it is clearly present. It also means that the massless and massive vector boson Lagrangians do contain fields of the other type via the still-implicit vector boson interaction terms. Because it is clear where all the important parts are, I decided that this would be a good compromise between clarity and compactness.
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
A clarification on tachyon condensation:
Tachyon condensation handles the tachyon problem at high energy in theories that are used for phenomenology. The first two theories discussed in this video only contain the scalar field used for breaking symmetry. There is therefore nothing for the tachyons present at high energy to decay into. Tachyon condensation therefore doesn’t take care of the problem for these theories. This is ok, however, because they aren’t used for phenomenology. In theories like the third example and ones like the standard model, which are used for phenomenology, tachyon condensation is free to take place on account of there being many particles that the tachyons can decay into. So when I say that tachyons don’t imply unphysicality at high energy, I mean that they don’t guarantee it. It ultimately depends on the theory.
Generalizing Gladstones Theorem To Complex Fields:
The way that I stated the Goldstone theorem in this video was that the number of broken generators (and Nambu-Goldstone bosons) is equal to the number of unbroken directions in isospin space, resulting from the zero isospin components in the new vacuum about which we were expanding the theory. This makes perfect sense when the scalar field is real, and there is therefore one field per component. How this could be correct for a complex scalar field, where there are two fields per component is a little less obvious. It turns out that the immediate generalization is to say that there are as many broken generators (and Nambu-Goldstone bosons) as there are fields set equal to zero in the vacuum about which we are expanding. However, we can always recast an N component complex scalar field as a 2N component real scalar field, in which case the original statement would apply again. So in a round about way, that statement of the Goldstone theorem is generally valid, even for a complex scalar field.
Take the U(1) example in this video. It includes a one component complex scalar field. The new vacuum about which we are expanding the theory is real. One field has therefore been set equal to zero in that vacuum, namely the imaginary component. From this and the Goldstone theorem, we would expect one broken generator, one Nambu-Goldstone boson, and one massive gauge field. This is exactly what we see.
We could always recast the U(1) theory as an SO(2) theory with a two component real scalar field, instead of a one component complex scalar field. The new vacuum would then have one zero component, and one real constant component, and the earlier statement of the Goldstone theorem would apply and produce the same answer.
One final note on the U(1)/SO(2) problem. One is used to seeing residual symmetry associated with zero isospin components in the scalar field, but in U(1)/SO(2) theory, there is only one generator to be broken, so there is no residual symmetry.
Cylindrical Cavity Resonances:
youtu.be/yjtbVcE2jsI
Cuboid Cavity Resonances:
youtu.be/mWKLuN3Jfwk
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
*l is a nonnegative integer
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
To be clear, more physics videos will be coming (this will eventually includes more quantum field theory videos), I am just producing more diverse content.
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou
Superfluid Helium Resonance Experiment video:
youtu.be/unUNQNmuvUQ
Quantum Field Theory Lecture Series:
youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou


