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2022-04-27: How the Higgs Mechanism Give Things Mass

  • 02:31: ... wavefunction from one point in space to the   next - local phase - doesn’t affect measurable  quantities - only relative phase ...
  • 03:09: ... that the laws of physics are invariant  under changes in local phase. The set   transformations that can change local phase ...

2020-11-04: Electroweak Theory and the Origin of the Fundamental Forces

  • 05:42: So there we go - we insisted on a symmetry - that the Schrodinger equation is invariant to changes in the local phase of the wavefunction.
  • 06:20: ... is the magnitude of the wavefunction, and the rotation amount is our local phase ...
  • 08:50: ... in the Schrodinger equation so that it would no longer be invariant to local phase ...

2018-11-07: Why String Theory is Right

  • 08:35: ... the Schrodinger equation that fixes these phase differences preserving local phase ...
  • 11:07: ... as local phase invariance required us to add the electromagnetic field to the ...

2018-07-11: Quantum Invariance & The Origin of The Standard Model

  • 05:16: This position dependent phase shift is called a local phase shift, instead of a global phase shift.
  • 05:21: We'll try this because, well, we already know that the magnitude squared of the wave function should still stay the same under local phase shifts.
  • 05:38: ... if we do a local phase shift, say, only this point here, only that location changes, as if it ...
  • 05:50: If you allow this sort of local phase shift, you can change each point in a different way and really mess up the wave function.
  • 06:08: Among other things, messing with local phase really screws up our prediction for the particle's momentum.
  • 06:19: Change the shape of that wave function with local phase shifts and you actually break conservation of momentum.
  • 06:26: Local phase is not a gauge symmetry of the basic Schrodinger equation.
  • 06:38: Just for funsies, maybe we can change the Schrodinger equation to find a version that really is invariant to local phase shifts.
  • 07:34: ... we've discovered that the only way for particles to have local phase invariance is for us to introduce a new fundamental field that pervades ...
  • 08:24: Any particle that has this kind of charge will interact with and be affected by the electromagnetic field and be granted local phase invariance.
  • 08:35: In order to have this particular type of local phase invariance, particles must possess electric charge.
  • 08:48: In this case, the symmetry is local phase invariance and the conserved quantity is electric charge.
  • 09:41: It turns out that local phase invariance is just the simplest of the larger suite of gauge symmetries of the standard model.
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