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More specifically, |i = |0; k1 |0; k2 , f | = 0; −k3 | 0; −k4 |. 1. For any D it includes D(D − 1)/2 − 1 positive-norm states transforming in the spin 2 representation of the little group SO(D − 1). Working in the rest frame of such a state, the S-matrix elements involved in (16) are fixed by SO(D − 1) invariance and (anti-)linearity in the polarization matrix a: a|S|0; k1 |0; k2 ∝ a∗ij k1i k2j , 0; −k3 | 0; −k4 |S|a ∝ akl k3k k4l . (18) Summing over an orthonormal basis in the space of symmetric traceless matrices yields the contribution of these states to (16): 2 k3k k3l .

B) There are four tree-level diagrams that contribute to four-boson scattering in Yang-Mills theory: the s-channel, the t-channel, the u-channel, and the four-point vertex. 12). 14), and the f abc are the gauge group structure constants: f abc = Tr [λa , λb ]λc . (49) We can therefore re-write (47) in the following form: − igo2 e1 · e2 e3 · e4 (2π)26 δ26 ( α′ ki )Tr λa1 λa3 λa2 λa4 + λa1 λa4 λa2 λa3 (50) i 1 − (λa1 λa2 λa4 λa3 + λa1 λa3 λa4 λa2 + λa1 λa2 λa3 λa4 + λa1 λa4 λa3 λa2 ) . 2 Of the three diagrams that contain three-point vertices, only the s-channel diagram contains a term proportional to e1 · e2 e3 · e4 .

0 ∞ ′ = i

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A solution manual for Polchinski's String Theory by Headrick M


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