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MathPrinceps's profile
Laurens Gunnarsen
Laurens Gunnarsen
Laurens Gunnarsen
@MathPrinceps

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Laurens Gunnarsen

@MathPrinceps

Mathematical physicist and mentor to mathematically talented youth. Talent is that which bridges the gap between what can be taught and what must be learned.

Joined June 2012

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    1. 〈 Berger | Dillon 〉‏ @InertialObservr 5 May 2019
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      An extremely useful relation between the Kronecker delta and the Levi-Civita symbol. 👉The brackets mean that we completely anti-symmetrize in the indices m,npic.twitter.com/Hp8tK8qZ3D

      2 replies 5 retweets 34 likes
    2. Laurens Gunnarsen‏ @MathPrinceps 5 May 2019
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      Replying to @InertialObservr

      Holds only in two dimensions.

      2 replies 0 retweets 1 like
    3. 〈 Berger | Dillon 〉‏ @InertialObservr 5 May 2019
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      Replying to @MathPrinceps

      that's what I get for working in SL(2,C) for too long

      3 replies 0 retweets 1 like
    4. Pascal Kwanten‏ @pascalkwanten 5 May 2019
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      Replying to @InertialObservr @MathPrinceps

      Look also for the SL(2,C) gauge theory of gravity by Moshe Carmeli. He considers gravity as an SL(2,C) Yang-Mills theory in which he recovers the Newman-Penrose (NP) equations (also used to study e.g. gravtitational waves). He formulates GTR in concise elegant 2-spinor formalism.

      1 reply 0 retweets 1 like
    5. Laurens Gunnarsen‏ @MathPrinceps 5 May 2019
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      Replying to @pascalkwanten @InertialObservr

      Alas, these things never work. They always come to grief over soldering forms. GR is not a gauge theory in the usual sense. Its symmetries are not internal. The soldering forms, and the torsion-free requirement which inevitably alludes to them, are the canaries in the coal mine.

      2 replies 0 retweets 1 like
    6. Nova Introvert‏ @NovaIntrovert 6 May 2019
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      Replying to @MathPrinceps @pascalkwanten @InertialObservr

      Mr Laurens Gunnarsen, could you please kindly clarify what you said a bit more? Do you have more lead, or? Thank you.

      1 reply 0 retweets 1 like
      Laurens Gunnarsen‏ @MathPrinceps 6 May 2019
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      Replying to @NovaIntrovert @pascalkwanten @InertialObservr

      The fundamental dynamical variables of gauge theories are connections on principal fiber bundles over spacetime. Attempts to make GR fit into this framework tend to focus on the frame bundle. But the frame bundle is no ordinary fiber bundle over spacetime. It's extremely special.

      9:06 AM - 6 May 2019
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      • Nova Introvert 〈 Berger | Dillon 〉 Pascal Kwanten
      6 replies 1 retweet 2 likes
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        2. Laurens Gunnarsen‏ @MathPrinceps 6 May 2019
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          Replying to @MathPrinceps @NovaIntrovert and

          In particular, the frame bundle is "soldered" to the base manifold (i.e., spacetime) in a way that simply has no counterpart for other principal fiber bundles. It is exactly this feature that makes it possible to speak of torsion-free connections -- the only kind relevant to GR.

          1 reply 0 retweets 2 likes
        3. Laurens Gunnarsen‏ @MathPrinceps 6 May 2019
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          Replying to @MathPrinceps @NovaIntrovert and

          This soldering of the frame bundle to spacetime has a thousand profound ramifications, none of which can be naturally accommodated into the normal framework of gauge theory. And it doesn't help to replace the frame bundle by its double-cover, the spin bundle. It too is soldered.

          1 reply 0 retweets 1 like
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        1. 〈 Berger | Dillon 〉‏ @InertialObservr 6 May 2019
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          Replying to @MathPrinceps @NovaIntrovert @pascalkwanten

          Very nice explanation

          0 replies 0 retweets 1 like
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        1. Nova Introvert‏ @NovaIntrovert 6 May 2019
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          Replying to @MathPrinceps @pascalkwanten @InertialObservr

          Thank you for your clarification, Mr Laurens Gunnarsen. Heard about GR roughly 15 years ago, and it has been something sacred since. It took a long way for someone who grew up in a remote corner of the earth to finally understand it, at least a bit. /1

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        1. Nova Introvert‏ @NovaIntrovert 6 May 2019
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          Replying to @MathPrinceps @pascalkwanten @InertialObservr

          It feels more or less smooth and sound to learn GR when a student who has not run onto accidents along his education, but a lot harder for those who are derailed. Anyway, through shear passion, determination, and persistence, GR is not that hard. 2/

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        1. Nova Introvert‏ @NovaIntrovert 6 May 2019
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          Replying to @MathPrinceps @pascalkwanten @InertialObservr

          Mr Laurens Gunnarsen, I don't intend to bother you more but, will it be convenient for you to tell me some advisable textbooks/papers on what you clarified here, so that I can try dig deeper when I have time with hope that maybe one day I might have better understanding on GR? 3/

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        1. Nova Introvert‏ @NovaIntrovert 6 May 2019
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          Replying to @MathPrinceps @pascalkwanten @InertialObservr

          Mr Laurens Gunnarsen, what you clarified here deeply intrigued me & sparked my interest. Perhaps it will not surprise you if Nova admit that Nova does not (yet) understand what you said here. 4/

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