 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
Xl = X2 = in Visual Studio .NET
Xl = X2 = PDF417 2d Barcode Decoder In .NET Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in VS .NET applications. Generate PDF 417 In Visual Studio .NET Using Barcode printer for VS .NET Control to generate, create PDF417 image in .NET framework applications. + 112X
Decode PDF 417 In .NET Framework Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in VS .NET applications. Drawing Bar Code In VS .NET Using Barcode encoder for .NET Control to generate, create barcode image in .NET framework applications. = 111Xl + 112X2
Barcode Recognizer In VS .NET Using Barcode recognizer for VS .NET Control to read, scan read, scan image in .NET applications. Print PDF417 In C#.NET Using Barcode generation for .NET Control to generate, create PDF 417 image in VS .NET applications. (1037) PDF417 Creation In Visual Studio .NET Using Barcode creator for ASP.NET Control to generate, create PDF 417 image in ASP.NET applications. PDF417 Printer In Visual Basic .NET Using Barcode generation for .NET framework Control to generate, create PDF417 2d barcode image in .NET framework applications. X  111X
Encoding Code39 In .NET Framework Using Barcode generator for Visual Studio .NET Control to generate, create Code39 image in VS .NET applications. Paint Matrix Barcode In Visual Studio .NET Using Barcode maker for .NET framework Control to generate, create Matrix Barcode image in Visual Studio .NET applications. a transformation with unit jacobian, and write the reduced BetheSalpeter amplitudes as XP(Xl, X2) = e iP . x Xp(x) (1038) xAxt, X2) = e iP . x Xp(x) According to (1033) X and X are not to be confused with wave functions but stand rather for generalized form factors. The normalization conditions are therefore not straightforward, since they involve the relative time variable Xo. This innocentlooking question has been the subject of a long elaboration. The role of normalization is, of course, to provide the correct relation between the X function and the fourpoint Green function. Furthermore, it is essential in selecting the proper solutions to Eq. (1035). We return to the inhomogeneous Eq. (1029). Introducing the overall momentum of the pair (1,2) through Draw Linear In .NET Using Barcode generator for .NET framework Control to generate, create Linear Barcode image in .NET framework applications. Drawing Leitcode In .NET Using Barcode printer for .NET framework Control to generate, create Leitcode image in .NET framework applications. S(12)(X 10 X 2, 1, Y2 [p)=fd4aeip.aS(12)(X 1 +a, x +a"y y) 'y 2 ,10 2 GS1 128 Drawer In VS .NET Using Barcode creator for Reporting Service Control to generate, create EAN 128 image in Reporting Service applications. EAN13 Supplement 5 Generator In None Using Barcode creation for Font Control to generate, create EAN13 image in Font applications. QUANTUM FIELD THEORY
Draw Bar Code In Java Using Barcode maker for BIRT Control to generate, create barcode image in Eclipse BIRT applications. Creating Code 3 Of 9 In None Using Barcode maker for Microsoft Excel Control to generate, create Code 3 of 9 image in Microsoft Excel applications. the bound state and its CPT transform contribute a pole in the variable p 2 : Printing GS1 128 In Java Using Barcode generation for Java Control to generate, create UCC128 image in Java applications. Draw UCC.EAN  128 In ObjectiveC Using Barcode printer for iPad Control to generate, create GS1 128 image in iPad applications. S(12)( . [P) _ iXP(Xlo X2)jp(ylo Y2) Xt, X2,Y1, Y2 p 2 _ M2 + ie
Painting Code 128 Code Set C In None Using Barcode drawer for Font Control to generate, create Code 128B image in Font applications. Generating EAN13 In C#.NET Using Barcode maker for Visual Studio .NET Control to generate, create EAN13 Supplement 5 image in Visual Studio .NET applications. (1039) with R regular in the vicinity of p 2 = M2. The factorization property of the pole residue is crucial for the interpretation in terms of bound state and has to be suitably generalized in the case of degeneracies. We iterate the equation (D + V)S(12) = 1 in the form S(12)(D + V)S(12) =  S(12l, insert (1039), and use the fact that (D + V)X = i(D + V) = 0 to compare the residues of both sides at p2 = M2. The result is symbolically i(D + V)X . . I1m 2 2 = I P  M
p2 .... M2
or, equivalently, the covariant expression
i[a!/l (D + V) 2iP/l
(1040) where the lefthand side involves an integral over relative variables. In general the normalization condition depends on the "potential" Vas opposed to the nonrelativistic case. It is useful to have these equations also written in momentum space. Let p denote the conjugate variable to x. According to (1037) we have + P2
(1041) where P1 = 1]lP + P and P2 = 1]2P  P refer to momenta carried by the fields <P1 and <P2 (Fig. 105). We have here no natural definition of the relative momentum as given by the separation of variables in a nonrelativistic motion, which results from the specific choice 1]1.2 = m1,2/(m1 + m2). In the relativistic case this choice may, however, be a good candidate for the purpose of comparison. Using the same symbols for the Fourier transformed quantities and taking translational invariance into account, we have xp(p) = e ip . XXp(x) d4 x
[(1]l P
+ p  miJ [(1]2 P  p)2  m~J Xp(p) + (~~~ V(p, p'; P)xp(p') = 0 p)2  jp(P) [(1]1 P
+ p  miJ [(1]2 P  m~J + (~~~ jp(p') V(p', p; P) = (1042) 0 The exchange of a scalar particle of mass p and coupling constants gl and g2 to particles 1 and 2, that is, such that the corresponding interaction lagrangian INTEGRAL EQUATIONS AND BOUNDSTATE PROBLEMS
pz = 'T/zP P Pz
Figure 105 Homogeneous equation for the boundstate amplitude X.
Yin! = (g1 <pi <P1
+ g2 <pi <P2)<P, leads in the Born approximation to
, Vl (p, p ; P) ig l g2 p  p')2  J1 2
+ It; . independent of P. Explicitly, the normalization condition reads
f(~~4 (~~~
jp(p') a!/l {[l]lP
+ p  miJ [(1]2 P  p)2  m~J(2n)4b4(p  p') (1043) + V(p', p; P)}xp(p) = 2iP/l
With Eqs. (1035) and (1040), or equivalently (1042) and (1043), we have now the basic ingredients to study some definite models. 1022 The Wick Rotation
Boundstate equations are derived in Minkowski space. In his early study, Wick was led to an analytic continuation to euclidean variables which was at the origin of the Wick rotation. It is easy to justify this procedure perturbatively, i.e., precisely, ignoring the possibility of new singularities such as those investigated here. Some care is required in order to extend it to the present situation. The essential physical point is to insure that stability criteria are met. Of course, the desirability of using this trick is to bring the equation in a form convenient for a simpler analysis. Let us proceed in a straightforward manner by writing, for X = 0, xp(x) = B(xO) f(x, P) jp(x)

