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Pauli spinors in such a way in VS .NET
Pauli spinors in such a way Decoding PDF 417 In .NET Framework Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in .NET framework applications. PDF 417 Maker In .NET Framework Using Barcode generator for Visual Studio .NET Control to generate, create PDF417 2d barcode image in .NET framework applications. A) = ;=:P,=+=M= (X(A)) Recognizing PDF417 2d Barcode In .NET Framework Using Barcode recognizer for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications. Barcode Creation In Visual Studio .NET Using Barcode creator for .NET Control to generate, create barcode image in .NET applications. , j2M(M
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(5196) As was already mentioned, parity diagonalizes the matrix f).I0).2 in such a way that
/!~2,1/2 f! 1/2,1/2 = 2e i
J . sin i5 J , The phase shifts 15 J, are real below the inelastic threshold and correspond to the scattering in the channel of total angular momentum J and parity ( _1)1+ 1/2. In nonrelativistic notation these states would be obtained from welldefined orbital angular momentum I with J = I i so that the corresponding phase shifts are also traditionally denoted 15,,+ and i5l+ 1, respectively. Let us now use the explicit formula for the Wigner f.& functions; + !)d{/2,1/2 = cos:2 (Pi+ 1/2 Pil/2) (5197) + !)d'I/2,1/2 = 8 sin:2 (Pi+ 1/2 + Pil/2) ELEMENTARY PROCESSES
With the I notation ((jJ,+ == (jl,+, (jJ, == (jl+ 1,) this yields the following expansions
fl(cos 8) Pi+ I(COS 8)ji,+  PiI(cos 8)ji,_ Pi(cos 8)(ji,+  ji,) (5198) h(cos 8) = e ib /, sin bz, ji, =q
Of course, for I = 0 the only surviving amplitude isfo,+. The question of subtractions in the dispersion relations should now be investigated. We postpone some general statements until the next subsection except to say that in pionnucleon scattering it can be shown that the only amplitude requiring a subtraction is A( +). A classical application of Eqs. (5190) is to the determination of the effective coupling constant. The principle of the method is to evaluate accurately from lowenergy phase shift analysis the B amplitude for n+ proton elastic scattering (it is, in fact, dominated by the J = i, T = i resonance) and to compare its real part in the forward direction with the value given by the dispersion integral. The latter is also dominated by its lowenergy contribution so that the approach is consistent. The value quoted by Hamilton and Woolcock is 4n \ 2M
~ (gnNNfl)2 = + 0.002 (5199) Dispersion integrals playa leading role in disentangling the various phase shifts at intermediate energies. As an exercise we suggest extending the formalism to the tchannel reaction nn ..... N N. 535 Momentum Transfer Analyticity
In the sequel, we disregard the spin of the external particles. Even though it is not a straightforward matter to include it, this can be done without modifying the results. Instead of using as a starting point of our discussion a reduction formula involving a particle in both the initial and final states, as we did in Sec. 532, let us rather reduce two initial particles in an elastic process with momenta PI and ql and associated fields t/J and <p. Thus we would initially write the connected Smatrix element (P2,q2[S[Phql\ =  dx 4 d4y ei(p,.x+q,.y) (Ox
+ ml)(Oy + m;)(P2,q2[ Tt/J(x)<p(y) [0), (5200) Returning again to the derivation of this formula, we observe that we might as well have used a retarded commutator instead of a chronological product in the physical region of the elastic process. Dropping inessential contact terms, we may therefore consider the replacement (with j and j", the sources of the t/J and <p fields) + mlj(Oy + m;) (P2, q2[ Tt/J(x)<p(y) [0), ..... (pz, q2[ 8(xO + q2 PI  ql)i5!i
yO) [j (x), j",(y)] [0 \ (5201) Taking momentum conservation into account, we obtain
(P2, q2[ S [Ph ql \ = (2n)4 (j4(P2 :TIi = i
d4x ei(q, p,) x/2 (P2, q2[ 8(XO{j G} j",( ~)]10), (5202) This representation shows that :T is analytic in the variable q = (ql  PI)/2, as follows from the JostLehmannDyson formula, and we may repeat an analysis similar to the one given for forward scattering. We take the total incoming momentum P = PI + ql as a time axis. Thus we shall work in the center of mass frame and exploit (5202) to obtain analytic properties in the cosine of the

