 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
f0(cp) exp in Visual Studio .NET
f0(cp) exp PDF417 2d Barcode Scanner In .NET Framework Using Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in VS .NET applications. PDF417 Generation In .NET Using Barcode generation for .NET framework Control to generate, create PDF417 2d barcode image in Visual Studio .NET applications. d4 x {i(ocpf  Reading PDF 417 In .NET Framework Using Barcode decoder for .NET Control to read, scan read, scan image in VS .NET applications. Painting Barcode In VS .NET Using Barcode creation for Visual Studio .NET Control to generate, create barcode image in Visual Studio .NET applications. ~2 [m
Recognizing Barcode In VS .NET Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications. Creating PDF417 In C# Using Barcode creation for .NET framework Control to generate, create PDF417 2d barcode image in VS .NET applications. + VI/(cpo)] PDF417 Maker In .NET Framework Using Barcode creator for ASP.NET Control to generate, create PDF 417 image in ASP.NET applications. PDF417 2d Barcode Generator In Visual Basic .NET Using Barcode encoder for Visual Studio .NET Control to generate, create PDF417 2d barcode image in .NET framework applications. cpP V(P)(CPo)}) p! (9109) Code 128 Code Set C Drawer In Visual Studio .NET Using Barcode generation for .NET framework Control to generate, create Code 128 Code Set C image in VS .NET applications. Linear Barcode Maker In Visual Studio .NET Using Barcode creator for .NET Control to generate, create 1D Barcode image in .NET applications. p : 3 Generating GS1 DataBar14 In .NET Framework Using Barcode generation for Visual Studio .NET Control to generate, create GS1 DataBar image in Visual Studio .NET applications. RM4SCC Creator In VS .NET Using Barcode creator for .NET framework Control to generate, create RM4SCC image in .NET framework applications. The new quadratic part is
ECC200 Drawer In Java Using Barcode generator for Java Control to generate, create Data Matrix 2d barcode image in Java applications. Scanning Code 128B In Visual C#.NET Using Barcode decoder for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications. d x {i(ocpf  Print Code128 In .NET Using Barcode creator for Reporting Service Control to generate, create Code 128 Code Set A image in Reporting Service applications. Code 128C Scanner In Java Using Barcode decoder for Java Control to read, scan read, scan image in Java applications. ~2 [m
Encoding Code 39 Extended In Java Using Barcode maker for Java Control to generate, create Code 39 Extended image in Java applications. Print ANSI/AIM Code 128 In Java Using Barcode drawer for Java Control to generate, create Code 128 Code Set B image in Java applications. + VI/(CPo)]} =  Decoding Barcode In Java Using Barcode Control SDK for BIRT reports Control to generate, create, read, scan barcode image in BIRT reports applications. Generate Bar Code In Java Using Barcode printer for BIRT reports Control to generate, create barcode image in Eclipse BIRT applications. d x icp[O
+ m 2 + VI/(cpo)]~
(9110) QUANTUM FIELD THEORY
and leads to a nontrivial propagator through its dependence on <po. To obtain the h expansion let us rescale the field as <p + h 1/ 2 <p so that Z(j) = eO,Ul/h
= e(i/h)I('Po,j) f0(<p) exp (i
d4 x {!(O<P  ~2 [m
+ VI/(<po)] (9111) p ::3 hP2 / <pP V(P)( <po)}) p! Wick's theorem applied to (9111) yields non vanishing contributions only for even polynomials in <po Only integer powers of h will therefore occur in the loop expansion. From Eq. (9111) we read that the leading term (order hO) to Gc(j) is I( <Po, j). Let us compute the next term. The integral over the quadratic part yields f0(<p) exp { i
d4 x <p[D
+ m2 + VI/(<po)]<P} = (Det Ko 1 K V )1/2 (9112) {Dx+m2+ VI/[<Po(x)]}t5 4 (xy) K o = (Ox
+ m2)t5 4 (x  As in Chap. 4, we use capital letters for determinants and traces of operators of infinite dimension. The inverse of Ko, introduced by the normalization, has to be chosen as GF(x  y). Hence Ko1Kv = t5 4 (x  y) + GF(x = eTr(InA) y)VI/[<po(Y)] Since a determinant may be written Det A we find
 iGc(j) (9113) = I(<Po,j) +:2 h Tr In [1 + GFVI/(<po)] + O(h2) (9114) To obtain 1(<p) we have to invert the relation
<p(x, J) = it5j(x) t5Gc(j) According to (9114) and (9108) <p is given to leading order by <Po up to corrections of order h. Moreover, since I is stationary at <Po we have I(<p,j)  I(<Po,j) = O(h2). Finally, we have to subtract Jd4 x <p(x)j(x) from iGc(j) to obtain r, given therefore by (9115) FUNCTIONAL METHODS
Figure 94 The effective potential to the oneloop order.
The perturbative interpretation of the second term is clear if we expand it as
~ Trln [1 + GFV"(cp)] 00 ( 1)"1 ih L Tr {[GFV"(cp)]n} n~ 1 2n
This is the sum of the contributions of oneloop diagrams made of n propagators  iGF(x  Y) and n vertices iV"(cp). It is depicted on Fig. 94 in the case of V(cp) = Acp4j4!. Notice that the factor 1j2n in front of each term of the sum is the symmetry factor of the corresponding diagram (n stands for the rotations, 2 for the reflection); similarly in the case of cp4 theory, the factor i in V"(cp) = Acp2j2 takes into account the symmetry between the two external legs attached to each vertex. This expansion may be carried out to all orders. The successive terms of Gc are represented by connected Feynman diagrams generated by the interaction term Lp;;'3hP/2I(cpPjp!)V(p)(cpo) with propagators obtained by the inversion of the kernel 0 + m 2 + V"(CPo). As far as qcp) is concerned, the result of the Legendre transformation is to select among the previous diagrams only the oneparticle irreducible ones, and to replace CPo everywhere by the arbitrary argument cp. Of course, any actual calculation has to face ultraviolet subtractions. In short, the steepestdescent or stationary phase method leads elegantly to the semiclassical expansion according to the number of loops. To go beyond perturbation theory requires either to expand around nontrivial extrema or to approximate the path integral in some utterly different way. We return to 1(<p). We know that its expansion in <p generates the oneparticle irreducible Green functions. As far as particle physics is concerned it is generally this aspect which is relevant. We may also insist on the role of 1(<p) as an effective action. Taking into account translation invariance we can find an expansion involving higher and higher derivatives in the field <p in the form (9116) QUANTUM FIELD THEORY
In (9116) the first term involves the sum of all proper functions at zero external momentum, the second sums all second derivatives at the same point, and so on. In principle the function q>(x) remains arbitrary. However, if we wish to compute Yeff only, we may satisfy ourselves with a calculation for a constant q> provided we can unambiguously factorize the fourvolume divergent integration over x. As an example let us extract Yeff up to order h from Eqs. (9114) and (9115). In general,

