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InertialObservr's profile
〈 Berger | Dillon 〉
〈 Berger | Dillon 〉
〈 Berger | Dillon 〉
@InertialObservr

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〈 Berger | Dillon 〉

@InertialObservr

PhD student of Theoretical Particle Physics @UCIrvine l @NSF Fellow l Physics & Math Animations l Patreon: https://www.patreon.com/inertialobserver …

DC → CA
youtube.com/c/InertialObse…
Joined August 2015

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    1. Bob (probably)‏ @knighton_bob 5 Nov 2019
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      Tbh I’ve taken 8 quantum field theory courses and I’m still not 100% sure what a Fermion is

      18 replies 19 retweets 333 likes
    2. 〈 Berger | Dillon 〉‏ @InertialObservr 5 Nov 2019
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      Replying to @knighton_bob

      the fundamental representation of the Poincaré group

      3 replies 0 retweets 18 likes
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    4. Bob (probably)‏ @knighton_bob 5 Nov 2019
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      Replying to @LambdaQG @InertialObservr

      The Lorentz group SO(3,1) is a symmetry group of relativistic mechanics. Quantum mechanically, the representations of this group that are interesting are those of the double cover, SL(2,C). The smallest irreducible representation of this group gives the “spin-1/2” representation.

      1 reply 0 retweets 1 like
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    6. Bob (probably)‏ @knighton_bob 5 Nov 2019
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      Replying to @LambdaQG @InertialObservr

      The double cover isn’t too hard to understand: SO(3,1) isn’t simply connected (not every loop can be contracted to a point). The Universal Cover (in this case, double cover) is the “smallest” group “containing” SO(3,1) that is simply connected. This happens to be SL(2,C).

      1 reply 0 retweets 0 likes
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    8. Bob (probably)‏ @knighton_bob 5 Nov 2019
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      Replying to @LambdaQG @InertialObservr

      Since overall phase doesn’t matter in quantum mechanics, we can look for representations that carry an extra phase, and these are called “projective” representations. It turns out that for most symmetries, the projective representations of a group can be written as regular...

      1 reply 0 retweets 1 like
    9. Bob (probably)‏ @knighton_bob 5 Nov 2019
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      Replying to @knighton_bob @LambdaQG @InertialObservr

      ...representations of its universal cover. This is the origin of why we study SU(2) instead of SO(3) in 3-dimensional systems. The rotation group SO(3) isn’t simply connected, and SU(2) is it’s universal cover, which is what is relevant in quantum mechanics.

      1 reply 0 retweets 1 like
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      〈 Berger | Dillon 〉‏ @InertialObservr 6 Nov 2019
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      Replying to @LambdaQG @knighton_bob

      We don’t QCD is an SU(3) gauge theory

      9:13 AM - 6 Nov 2019
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        2. 〈 Berger | Dillon 〉‏ @InertialObservr 6 Nov 2019
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          Replying to @LambdaQG @knighton_bob

          yea you can have global SO(3) symmetries and such .. you can even gauge it if you want

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          3. End of conversation

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