The mathematics of supersymmetry is utterly natural and deeply connected to all other mathematics. Whether it's relevant to physics is another question: time will tell.
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Replying to @johncarlosbaez @EricRWeinstein and
Eric: "The physics argument has always been that it must get used physically because it would be too weird to exist and not to be made use of." Physicists only bother with these arguments when they're not getting enough experimental data. They're better at experiments.
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I‘m reading your &
@skdh’s responses and don’t think Tweets are the right place to argue this. But I‘m still impressed how neither math nor physics has fully naturally accommodated fractional spin to my thinking. We find it everywhere but we still give a semi-‘magical’ treatment.2 replies 0 retweets 7 likes -
I don't see much magical about spin-1/2 particles. Wigner proved quantum symmetries correspond to projective unitary group reps. Classify the projective unitary reps of the Poincare group and out pop spin-1/2 particles. (I'm being sketchy here, of course!)
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I would say the complete correspondence between bosonic field theory and its fermionic analogs is wildly surprising to me.
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Replying to @EricRWeinstein @johncarlosbaez and
Shocking even. The operations don’t even look like each other (Berezin vs Bosonic integrals). I don’t think anyone has explained the perfection of the duality given how different the ledgers are.
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Hmm, everything about bosons and fermions looks alike to me - including the integration theory - with minus signs put in whenever you switch odd variables.
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Is there a lebesgue or riemmanian integration theory below the Berezin theory? I may just be ignorant.
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I'd say the analysis behind fermionic integration theory perfectly matches that behind the bosonic case except that the exterior algebra of a finite-dim vector space is finite-dimensional, which tends to make the integration in this case "too easy": http://math.ucr.edu/home/baez/bsz.html …
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Replying to @johncarlosbaez @EricRWeinstein and
One thing I don't think we understand is how the bosons and fermions fit together in the Standard Model. Supersymmetry proposes a simplistic solution: one fermion for each boson, with the same mass. But this is far from what we see. Someday we may think of something better.
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Gosh, I hope so. But I don't really expect to be here to see that.
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Replying to @MathPrinceps @EricRWeinstein and
Neither do I - despite tantalizing clues, which may be red herrings, like this: https://golem.ph.utexas.edu/category/2018/08/exceptional_quantum_geometry_a.html …
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