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A formulation of noncommutative M = 2 supersymmetric theories in terms of superfields was given in 34 Note that the scalar electrodynamics examined in the previous section can be considered as a bosonic part of AT = 2 NCSYM. The identification is evident: and cf>* corresponds to + and _, respectively. Also we should replace A by g and take a — — b = — 1. The fact that fields (j>± are not complex conjugate does not affect the performed calculations. 16) can be easily obtained from the Feynman rules for scalar electrodynamics (see Table 1) using the above mentioned identification.

E - The following analytic expression corresponds to the graph on Fig. 5:b _Nb(f)*< L5 "~ (2TTY f J V5b(p,k) d a K (fc2 +TO 2)(( A; + p)2+m2) ' ^- 1 U J where Nb is a number of graphs (Nb=8), P = P2+P4 = —pi ~P3 and Vsbip, k) is the trigonometric polynomial Vbb{p,k) — [Acos(k Ap2 + (-A; — P2) Ap±) + Bcos(p2 Ap4)cos(fc A P)] x [Acos(pi A (-k) +p3 A(k -pi)) + Bcos(pi Ap3) cos(fc A P)} . 10). Divergencies come from the terms AV^t of the polynomial Vst B2 AV5b = - y cos(pi A p3) cos(p2 A p 4 ) . The graphs Fig.

Overlaps |Vjy)e solves the overlap conditions XT{(T) e - Xr-i(ir - a) = 0 , Pr(

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lecture in plasma physics by Nogoya
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