We develop the idea for a new string field theory of ours that was proposed earlier in a very rudimentary form in a talk in the Symposium of Tohwa University [1]. The main point is to describe the system of strings in the Universe by means of the images of the derivatives of the right and left mover parts of the 26-position vector on the strings w.r.t. tau. The major progress since the Tohwa-talks [1] is to imagine a discretization of the variables on which right and left movers respectively depend. We then observe that, by using only the descritized even-numbered sites, we can set the commutation rules for second quantization without any contradiction. In fact we can quantize the objects described by these even numbered images. A light-cone frame description of the string field theory in this way is presented.
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