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ff(q) Iq= q = in Visual Studio .NET
ff(q) Iq= q = PDF417 Scanner In .NET Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in .NET framework applications. PDF417 Maker In .NET Framework Using Barcode generation for VS .NET Control to generate, create PDF417 image in Visual Studio .NET applications. iC(q) Reading PDF417 In .NET Framework Using Barcode scanner for .NET Control to read, scan read, scan image in VS .NET applications. Make Barcode In VS .NET Using Barcode drawer for .NET framework Control to generate, create bar code image in VS .NET applications. vanishes in a certain domain. This is the Fourier transform of the commutator
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Figure 58 The two hyperboloid sheets limiting the support of the commutator in momentum space. The unshaded area is the coincidence region denoted 'C. fourmomentum on the other side of the reaction. The statement of crossing symmetry will become meaningful if we succeed in showing that analytic continuation allows access to the coincidence region starting from physical values for the momenta. This property is a remarkable consequence of field theory. We denote it(q) the expression given in (5172) with q substituted for  if. and observe that it(q) is analytic in the backward tube, i.e., for 1m q a negative timelike vector. Thus f/(q) and it(q) have a priori disjoint domains of analyticity and coincide on a real domain 'f1. The celebrated edge of the wedge theorem, due to Bremermann, Oehme, and Taylor, allows us to conclude that f/ and it are analytic continuations of each other, and moreover that their common domain of analyticity is larger than the union of the forward and backward tubes and 'f1. If we were dealing with functions of one complex variable only, the problem would be easily settled. Indeed, if f (z) are analytic in the upper and lower complex z plane respectively and coincide ~n a segment of the real axis, a simple application of Cauchy's theorem proves that they are branches of the same analytic function. The coincidence points are in fact analyticity points. The present situation is obviously more complicated. Around each coincidence point there are holes corresponding to spacelike imaginary directions where neither t7 nor ff are defined. Hence the pictorial name "edge of the wedge." Moreover, analysis in several complex variables uncovers new properties without equivalence in the case of one complex variable. Such is the notion of a holomorphy envelope. A function of several complex variables analytic in a domain: can at least be extended to a domain ~::>: , with the property that through any of its boundary points we can find an analytic manifold, i.e., the set of zeros of an analytic function, lying entirely outside ~ except for the boundary point in question. This property is referred to as pseudoconvexity (in analogy with ordinary convexity), with analytic manifolds replacing planes. In the case at hand, even though a purely geometric construction of ~ is possible, an interesting representation generalizing the KiillenLehmann representation for the vacuum expectation value of the commutator is available to solve the problem. The reader may wonder whether the original analyticity domain, including the forward and backward tubes, was not enough in simple cases such as forward scattering with PI = P2 = P, ql = q2 = q. The following remark will dissipate doubts. Let a complex vector q lie on the mass shell and write q = qR + iq,. Then the condition m~ = q2 = q~  q7 + 2iqR'q, states that qR and q,

