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rune in Visual Studio .NET
rune PDF417 2d Barcode Scanner In .NET Framework Using Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in Visual Studio .NET applications. PDF417 Maker In VS .NET Using Barcode creator for Visual Studio .NET Control to generate, create PDF417 image in .NET framework applications. PI qJm
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(671b) We now construct the Legendre transform of Gc as follows. Let <Pc(x,j) be the functional of j defined through J <Pc(x,j) = iJj(x) Gc(j) (672) and let us assume that the relation <Pc(x) = <pix,j) may be inverted to yieldj(x) = jc(x, <Pc). This is possible at least as a formal series provided (JGc/Jj)lj=o = 0, which means that the onepoint function vanishes and [J 2 Gc/Jj(x)Jj(y)Jlj=o:;6 0. This is what we assume in the following. The subscript c in <Pc aims at reminding us that <Pc is an ordinary cnumber function, not to be confused with the quantum field <po The functional r( <Pc) is by definition W(<Pc) = [Gc(j)  i fd4Xj(X)<Pc(X)JI. _. J(X)  J,(X.'P,) (673) The factor i has been mtroduced for later convenience. From (673), it follows by differentiation with respect to <Pc(x) that . J I ~() T'( <Pc) = .o<Pc X d4Y {[JGc(j)  l<Pc(Y) . . . JMy,()  IJc (X, <Pc) <Pc)} .. y() ~ 'J Y J= J,('P,) u<pc X
The first term of the righthand side vanishes, owing to (672), and
. Jix, <Pc) Jr( <Pc) J<pix) (674) As is well known in the analogous instances of classical mechanics or thermodynamics, the Legendre transformation is involutive. We also notice that iT'(<pc) may be regarded as the value of Gc(j)  i Jd 4xj(x)<pc(x) (j and <Pc independent) at its stationary point inj. PERTURBATION THEORY
We want to show that r( ((>c) is the generating functional of proper functions r(xr, ... ,xn): r(({>c) L~ n.
d4X l ... d4xn r(n)(Xl,".' Xn)({>iXl) ((>c(xn) (675) where in the last equation use has been made of Eq. (674). Hence, the kernel [J2r/J({>c(y)J({>c(z)] is the inverse of i [J 2 GjJj(z)Jj(x)] !i=i,' We may now set ({>c = 0, according to the assumption that (JGc/Jj)!i=O = 0. The previous identity tells us that the connected twopoint function 2 )(z  x) =  [J 2 Gc/Jj(z)Jj(x)] !i= 0 is the inverse (for convolution) of the function  ir(2)(y  z) =  i[J 2r/J({>c(y)J({>c(z)]cp,=o From translational invariance r(2) depends only on the difference y  z and
d4z r(2l(y  Z)G~2)(Z  x) = iJ 4(x  y) (677) In momentum space, this reads
G(2)(p,  p)r(2)(p,  p) where the Fourier transforms of the r are defined as in Eqs. (620) and (621). Henceforth, we shall use shorter notations for the twopoint function G(2)(p) == G(2)(P, p), r(2)(p) == r(2)(p, p). If we write the former as

