Loop Variables and Gauge Invariant Interactions - I

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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40 pages, Latex. Revised version: some typos corrected. Final version to appear in Int. J. of Mod. Phys. A

Scientific paper

10.1142/S0217751X00001907

We describe a method of writing down interacting equations for all the modes of the bosonic open string. It is a generalization of the loop variable approach that was used earlier for the free, and lowest order interacting cases. The generalization involves, as before, the introduction of a parameter to label the different strings involved in an interaction. The interacting string has thus becomes a ``band'' of finite width. The interaction equations expressed in terms of loop variables, has a simple invariance that is exact even off shell. A consistent definition of space-time fields requires the fields to be functions of all the infinite number of gauge coordinates (in addition to space time coordinates). The theory is formulated in one higher dimension, where the modes appear massless. The dimensional reduction that is needed to make contact with string theory (which has been discussed earlier for the free case) is not discussed here.

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