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Re: Question about Paul Dirac

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Posted by DickT on December 06, 2002 at 08:27:27:

In Reply to: Question about Paul Dirac posted by sol on December 05, 2002 at 22:00:16:

Sol,

To get it out of the way, the i in the third matrix is the square root of -1. All of these matrices are complex, although the other three use only the real unit, 1 = 1 + 0i. The matrices act on complex vectors in four dimensional complex space. these vectors are actually Dirac spinors.

Now, the prehistory of strings. The very first string theory was Heisenberg's one dimensional quantum field theory back in the thirties. I believe I have heard that some work of Dirac's is a precursor to strings, but I don't know what it is.

String theory really began when Veneziano discovered the "dual channel model". Imagine you have a reaction that looks like a blob or cloud representing "we don't know", and two particles enter the cloud and two come out. Now if we imagine the two incomers exchanged a boson and produced the two outgoers, that could happen in two ways.


    \        /           \   /
     \      /             \ /
      ------         or    |
     /      \              |
    /        \            / \
   /          \          /   \

Veneziano wanted an amplitude formula that would cover both cases, which are equally likely. He found it in Euler's Beta Function. Nambu then pointed out that Veneziano's math could be interpreted as describing strings in 26 dimensional space, with the particles in the diagram coming out as vibrations of the string.

Regards,
Dick

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