M Theory Lesson 41

Recall that it is for 3×3 matrices that a Tao hexagon first arises in a diagram representing a sum of three matrices. One segment, or rather one matrix, is composed of the solid lines in the diagram This contrasts with the 2×2 case, for which only open dagger regions appear, and this may occur in three ways, depending on the orientation of the region. It is remarkable to realise that only in the 21st century do we finally return to Dirac’s original idea of the q-number. Heisenberg’s matrices were always representations of q-numbers, but not true numbers in themselves.

5 Responses so far »

  1. 1

    Doug said,

    Hi Kea,
    I found this interesting discussion of DIRAC’S QUANTUM MECHANICS, including q-numbers.


  2. 2

    L. Riofrio said,

    Hexagons seem to be everywhere in nature. This continues to hint at some deeper principle.

  3. 3

    Kea said,

    Thanks, Doug! Thanks, Louise. Yes, things are slowly becoming clearer.

  4. 4

    kneemo said,

    Kea, take a look at Ashoke Sen’s 1997 String Network paper. Essentially, one can construct a string lattice from three string junctions, resulting in a hexagonal honeycomb pattern.

  5. 5

    Kea said,

    Ah, nice, kneemo. As Sen says in the 1997 conclusion: at present the utility of the string network, besides describing BPS states in toroidally compactified type IIB string theory, is not clear. However, in future…

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