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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. Nikita Lisitsa‏ @lisyarus 11 Jul 2019
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      Nikita Lisitsa Retweeted 〈 Berger | Dillon 〉

      Representation theory of the group with 2 elements at workhttps://twitter.com/InertialObservr/status/1149413668905316352 …

      Nikita Lisitsa added,

      〈 Berger | Dillon 〉 @InertialObservr
      The hyperbolic Euler's identity actually trivially follows from the fact that any function can be split into: (1) An even part: [f(x) + f(-x)]/2 (2) And an odd part: [f(x) - f(-x)]/2 pic.twitter.com/UTwLJQKpVG
      Show this thread
      1 reply 1 retweet 10 likes
    2. 〈 Berger | Dillon 〉‏ @InertialObservr 11 Jul 2019
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      Replying to @lisyarus

      Yea! I think that the even and odd parts form irreducible representations of Z_2, right?

      1 reply 0 retweets 0 likes
    3. Nikita Lisitsa‏ @lisyarus 11 Jul 2019
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      Replying to @InertialObservr

      Yep, exactly! As do the symmetric/antisymmetric matrices or tensors, and so on. The formula f(x) = [f(x) + f(-x)]/2 + [f(x)-f(-x)]/2 is a a special case of decomposition into irreducible representations. The general case has an exact formula through character theory, too.

      2 replies 0 retweets 1 like
    4. 〈 Berger | Dillon 〉‏ @InertialObservr 11 Jul 2019
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      Replying to @lisyarus

      nice! I know that young tableux help for the decomposition of SU(N) groups, but are you saying that the characters can tell us the exact same thing for arbitrary groups?

      1 reply 0 retweets 0 likes
    5. Nikita Lisitsa‏ @lisyarus 11 Jul 2019
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      Replying to @InertialObservr

      I can't find a source right now, but once you know a character χ of an irreducible representation, the operator of projection on this type of irrep is always given bypic.twitter.com/N6NbuhfEew

      1 reply 0 retweets 1 like
      〈 Berger | Dillon 〉‏ @InertialObservr 11 Jul 2019
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      Replying to @lisyarus

      oh wow that's super useful!

      1:39 PM - 11 Jul 2019
      • 1 Like
      • Nikita Lisitsa
      1 reply 0 retweets 1 like
        1. New conversation
        1. Nikita Lisitsa‏ @lisyarus 11 Jul 2019
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          Replying to @InertialObservr

          (uh, I hope I didn't put it wrong)

          1 reply 0 retweets 2 likes
        2. Valentin Fadeev‏ @ValFadeev 11 Jul 2019
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          Replying to @lisyarus @InertialObservr

          Did someone say "source"? The man himself, and P. A. Grilled here, respectively. And now I want to know so much more about these than I have time for...pic.twitter.com/fMRJM6EfCx

          1 reply 0 retweets 2 likes
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