By Enrico Fermi

The most strategy of this two-volume treatise is that it offers with the interaction among thought and scan. other than the most textual content which bargains with systematic exposition of the topic, reference is made to the remedy of experimental information in sections labelled "illustrative examples"

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**Example text**

Next, we translate: B' -t B" = B' - K1/2 A, W' -t w" = w' + 01/2r/, W' -t W" = w' + 0 1/ 27]. The only term that will yield a contribution is the one containing a product of three sources. J. (0 i])a (x)) Jabc(K A)~(X )(07)h(x), This property may also be deduced in the canonical formalism by the identification of the propagators as Green's functions of the corresponding differential equations. Chapter 2 42 and therefore (Twa(xdWb(x2) = Xl. B~(X3))ol J d4 PI J order 9 (27r)4 e . abcP1v, P3 again as expected.

12) generates the Feynman rule given in Appendix E and to be used in Sect. 6. 7 The Background Field Method The functional formalism allows a simple introduction of the background field method, an elegant and powerful formalism whereby gauge invariance of the generating functional (in a sense to be specified) is preserved. The method was first introduced by DeWitt (1967), and was extended by 't Hooft, Boulware and Abbott. In our exposition we will follow the very readable account of the last author (Abbott, 1981), which may also be consulted for more details and references.

A functional of (classical) fermion fields will be of the general form F[1jJ] = Ko + + J J dXl Kl (xd1jJ(xd + ... dXl ... dX n Kn(Xl, ... , Xn)1jJ(Xl) ... 1jJ(xn) + ... , where Kl is an anticommuting function and the K n , n 2: 2, may be taken as fully antisymmetric in their arguments. The extension of the definition of[1jJ] = lim F[1jJ o1jJ E--+O + cOx] E - F[1jJ] ' laThe corresponding structure is known as a Grassmann algebra in the standard mathematical literature. More details may be found in the treatise of Berezin (1966).