String Theory


For about two years now, I have been doing work on String Theory in the half-string language with Dr. Abdulmajeed Abdurrahman. We have come up with a number of interesting results and questions, and are working on two papers. Right now I would be particularly interested if anyone has good formulae for the Neumann Coefficients for 3-string interaction, as we have been unable to find or derive ones that give accurate results to the Ward Identities. This leads me to think that the Ward Identities might be somehow incorrect, given the amount of agreement between our derived formulae and the published ones. Unfortunately, to say for certain that the Ward Identites are incorrect is a bold statement to say the least, and is not one that can be taken lightly. Therefore, the work towards the Ward Identites is available only on request, because I do not want to add to any confusion by putting work here that I believe is wrong or doesn't work. Below is a sample of more complete and correct work and notes to date.

Initial TrainingI took notes as I went through the derivations of the basics of Half-String Field Theory. These are those notes.
Full-String from Half-StringOne of the major focuses of our research is the creation of an operator to bridge the gap between the half-string and full-string language. Here is the derivation of such an operator at a very high level.
Full-String from Half-String Integral
Companion Notebook		Dr. Abdurrahman took a lower-level approach to the above, and presented the inversion to me. I have here converted the necessary sum into an integral which he is currently working on evaluating.
Infinite Matrix Inversion ApproximatorI wrote a program to approximate the inverse of an infinite matrix in the case where the infinite edges converge to zero.
An Interesting Identity Courtesy of the Ward IdentitiesI found that if the Ward identities hold, I get an interesting identity on the 2F1 function.