from the lowest order correction to a gluon propagator represented by a single solid line
segment on a world sheet strip as in Fig. 3-1.
ki
/ M
Figure 3-1. One loop gluon self energy. Because of time translation invariance only the
difference k = k2 k, is important.
With the conventions used here, the result analogous to Eqs. (52) and (53) of that
article, for fixed kl, k2, I with k = k2 k, > 1 and 0 < 1 < M, reads
92 k{2 2 t[ I- -(2+N8-Nf)r t- )]} (31)
87 2k2 I M-1 M 2 M M
where u = e-p2a/2Mm. This must be summed over I and k, and k2. For brevity in the
discussion of these sums, denote by A(l, M) the contents of the curly braces in the last
equation. Now consider the one loop correction to the gluon propagator, propagating
K T/a time steps. The loop starts at time k1a and ends at k2a and is positioned at
p+ = ml. Before introducing the counter-term we have the following expression for the