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and This means that close to threshold in .NET
and This means that close to threshold Recognize PDF 417 In VS .NET Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in Visual Studio .NET applications. Paint PDF417 2d Barcode In Visual Studio .NET Using Barcode maker for VS .NET Control to generate, create PDF417 2d barcode image in VS .NET applications. _ ffi iV(q) =  4mamb
PDF 417 Decoder In .NET Framework Using Barcode scanner for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications. Making Bar Code In VS .NET Using Barcode creator for .NET Control to generate, create barcode image in .NET framework applications. (7127) Recognizing Barcode In VS .NET Using Barcode decoder for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications. Print PDF 417 In Visual C# Using Barcode generation for .NET Control to generate, create PDF417 image in Visual Studio .NET applications. (7128) Paint PDF417 In .NET Framework Using Barcode creator for ASP.NET Control to generate, create PDF 417 image in ASP.NET applications. Make PDF417 2d Barcode In VB.NET Using Barcode generation for .NET Control to generate, create PDF417 2d barcode image in .NET framework applications. where _q2 can be identified with the square relativistic momentum transfer q2 = (Pa  p~)2, and the center of mass energy square s = (Pa + Pb)2 is taken equal to (ma + mb)2. From (7123) we can compute the amplitude ffi to order g2 as represented in Fig. 716. This is again a oneloop diagram with a strong ultraviolet divergence. A theory based on (7123) is not renormalizable due to the dimensionality of the coupling constants. However, we agreed to use it only as a phenomenological description and as such to any order we may perform a finite number of ultraviolet subtractions without modifying the longrange behavior of V which we intend to find. Therefore for our purpose we are safe. The elementary contraction needed to apply perturbation theory is Painting Code 128C In VS .NET Using Barcode generation for .NET Control to generate, create Code128 image in VS .NET applications. Painting EAN 13 In .NET Using Barcode drawer for .NET Control to generate, create EAN 13 image in VS .NET applications. Kpv,pa(k) Drawing UCC128 In Visual Studio .NET Using Barcode printer for .NET framework Control to generate, create EAN128 image in Visual Studio .NET applications. Drawing USS Codabar In .NET Using Barcode encoder for .NET Control to generate, create Rationalized Codabar image in .NET applications. kpkpg ya  kykpg pa  kpkagvp + kykag pp
Encoding 1D In Visual C#.NET Using Barcode printer for .NET Control to generate, create Linear 1D Barcode image in .NET framework applications. UPC  13 Printer In ObjectiveC Using Barcode creator for iPad Control to generate, create EAN13 image in iPad applications. (7129) Create Data Matrix 2d Barcode In None Using Barcode printer for Office Excel Control to generate, create Data Matrix image in Microsoft Excel applications. Data Matrix ECC200 Maker In Visual Studio .NET Using Barcode generator for ASP.NET Control to generate, create DataMatrix image in ASP.NET applications. Before any subtraction the Feynman rules provide us with an amplitude ffi of the form
Painting Data Matrix 2d Barcode In Java Using Barcode creation for Java Control to generate, create Data Matrix 2d barcode image in Java applications. Decode EAN / UCC  13 In .NET Using Barcode reader for .NET Control to read, scan read, scan image in .NET applications. ffi d(k, k') UPC Code Creation In .NET Framework Using Barcode creator for Reporting Service Control to generate, create UCC  12 image in Reporting Service applications. Draw Code 39 Extended In Java Using Barcode generator for BIRT Control to generate, create Code 39 image in BIRT reports applications. d4k d4k' o4(k + k'  q) (2n)4(k 2 + ie)(k,2 + ie) d(k, k') = 8g~g~Kpv,pa(k)KPv,pa(k') + [4g1g~(p~p'p + ppp'~)Kay,pa(k)KPv,pa(k') + (a +> b)] + g1gWp~p'p + ppp'~)Kav,a'v'(k)KPv,P'v,(k')(p~,p'~' + p~,p,~,) + (k+>k')J (7130) A convenient way to perform the ultraviolet subtractions without modifying the longrange behavior follows from the observation that for fixed s = (Pa + Pb)2, ffi is analytic (and purely imaginary) along the semiaxis q2 < O. Its cut along the real axis arises from its real part and we are only interested in the vicinity of q2 = O. We therefore write = : dm 2
2 ffi (m ) R 2 . mqle
+ ~ffi(q2) (7131) RADIATIVE CORRECTIONS
Pb ~.... ....  P~ b
Figure 716 Interaction between neutral systems arising from electric and magnetic susceptibilities.
with I:lfii regular in the vicinity of q2 = 0 and M2 positive and arbitrary. Consequently, from (7126) and (7128) the asymptotic part of the potential will be given by (7132) We shall soon see that fiiR(q2) behaves as  A(q2)2 for q2 + 0 so that the dominant part of V will be obtained by taking the limit Mr + 00 in (7132), that is, Va,(r) 16n mambr
fro dx
x =
8n mambr
(7133) It remains to compute A. To do so we observe that each denominator in (7130) may be split into two terms according to I/(k 2 + ie) = PPlk 2  inb(F) where PP means principal part. This we abbreviate as P  inb. Up to the polynomial d the integrand in (7130) takes the form (P  inb)(P'  inb') = PP'  n 2bb'  in(bP' + b'P) This is, of course, nothing but the Fourier transform of [GF(x  y)F in configuration space with GF the Feynman propagator. The effect of d is then to act as a polynomial of derivatives on this quantity. Now if instead of using G} we were to use the product Gadv(x  y)Gret(x  y) with at most a support at x = y we would obtain by a Fourier transformation an illdefined polynomial of the momenta without contribution to the real part of fii. Consequently, as far as we are concerned, the replacement 1 1 k 2 + ie k'2 + ie + F 1 + i(kO/lkOI)e
1 k'2  i(k,oljk' l)e
would lead to zero. This means that we may subtract to the previous contribution the combination (P  ineb)(P' + ine'b') = PP' + n 2ee'bb' + in(Pe'b'  P'eb) with eb standing for (kO II kO i) b(k 2). The result is the quantity (PP'  n 2bb')  (PP' + n 2ee'bb') = n 2(1 + ee')bb' Note that 1 + ee' = 2 if kO and k'o are of the same sign and zero otherwise, and that the 15 functions project the photons onshell. For q2 > 0 the conservation of energy momentum k + k' = q implies that we may keep only one of the two possibilities kO > 0, k'o > 0, for instance. We have now (7134) This lengthy derivation is nothing but an application of the Cutkosky rules (Chap. 6) to this special case. Of course, fiiR as given by Eq. (7134) is a convergent quantity and we simply want its leading

