Deriving the Dirac Equation

Comments · 431

• RI

  @RichBehiel · 2 years ago · pinned

  Hey all, thanks for checking out this video! :)<br><br>While reviewing the video just now, I realized I probably should have been more clear about covariance and contravariance. This affects the sign of the momentum terms (more generally, the space-like terms), and is a perennial source of dropped minus signs 😅 The plus signs at <a href="https://www.youtube.com/watch?v=CbYFanAGsSM&amp;t=800">13:20</a> are due to using the contravariant Dirac matrices, three of which which absorb the minus signs, see the Wikipedia article “gamma matrices” for more info.<br><br>Anyway, the main idea I hope you’ll take away from this video is that the anticommutation relations for the Dirac matrices arise from taking the square root of the mass shell.

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• JI

  @jim2376 · 2 years ago (edited)

  Dirac was known for both the brevity and precision of his speech. At a conference he was lecturing and writing at a blackboard. A member of the audience said at the conclusion of Dirac&apos;s presentation, &quot;I don&apos;t understand your equation in the upper right.&quot; Dirac said nothing and returned to his seat at the table with other lecturers. After an uncomfortable silence, the conference moderator asked, &quot;Mr. Dirac, are you going to answer the man&apos;s question?&quot; Dirac: &quot;It wasn&apos;t a question. It was a statement.&quot;

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• SI

  @SirTravelMuffin · 2 years ago

  The &quot;I&apos;m letting the squares breathe...&quot; was genius for geometrically visualizing variables!

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• PE

  @peterhall6656 · 2 years ago

  Fun fact. Back in 1972 I was taught some mathematical physics by the late Joe Moyal. &nbsp;Joe was invited by Dirac to Cambridge during the World War 2 to discuss Joe&apos;s work on statistical foundatiions of quantim mechanics (there is a 1947 paper with Bartlett and Kendall which also deals with the issues). Joe met Dirac and I can say that I have shaken hands with someone who has shaken hands with Dirac.

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• SA

  @SafetySkull · 2 years ago

  A thousand jargon-filled wikipedia articles could not have given me the clarity I now posess thanks to this video. Thanks so much

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• X-

  @X-boomer · 2 years ago

  When the math is shouting “PARTICLES AREN’T FUNDAMENTAL, THEY’RE EMERGENT, YOU’RE JUST DOING EPICYCLES AGAIN”

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• FU

  @FunkyDexter · 2 years ago

  The reason the coefficients don&apos;t commute (so the opposite breathing squares cancel out) and why the coefficient squared are negative numbers, is because a spinor is a unit quaternion! In fact, the nature of spin is a bit less mysterious if instead of using Dirac matrices we use quaternions, for rotations on a 4D hypersurface :)

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• DI

  @dialgapalkia · 2 years ago

  This sort of accessible education will prove to be revolutionary.

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• BA

  @bastiaanvanhoorn6306 · 2 years ago

  The teacher I had for QFT was one of the best teachers i ever met, and yet, this is so much more insightful then what he ever managed on a blackboard. The visualisation is genius.

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• EV

  @evilotis01 · 2 years ago

  eigenchris&apos;s &quot;Spinors for Beginners&quot; series is a really good introduction to, well, spinors for beginners!

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• MA

  @mathnerd97 · 2 years ago

  Well, Diract went a different direction. When I saw those constraints, my brain immediately went &quot;quaternion&quot;

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• BY

  @ByteCat271 · 2 years ago

  ok now imagine that dirac imagined everything and much more but without a computer and today&apos;s technology.

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