Regularization and Minimal Subtraction

The results of the previous chapter are completely general. They are valid for any field theoretic renormalization scheme, i.e. independent of the specific choice of the renormalization factors, For quantitative calculations we of course have to specify the Z-factors, and as pointed out in Sect. 11,1, we have some freedom there. We will use the scheme of dimensional regularization and minimal subtraction . This scheme is most efficient for actual calcular tions, but its underlying basis is a little bit delicate, It needs some careful explanation. 

This statement should immediately meet with opposition. We have stressed before that the continuous chain model has a number of shortcomings. 

How then can it be used to construct the renormalized theory, finite for d 4 and valid for all temperatures  

Concerning the first two points the answer is that in some sense they compensate each other Working with the continuous chain model the purpose of renormalization is not to eliminate the microstructure dependence, which effectively is suppressed by the limit but to make the theory finite for 

Concerning the third point we note that the renormalized theory, expressed in terms of u, does not know whether the underlying bare 

As formulated in the previous chapter, renormalization proceeds by first introducing according to Eq. (11.1), thereby absorbing the leading mi-crostructure dependence into the renormalization factors. In a second step the limit 0 is taken in the renormalized Greensfunctions to eliminate 

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In field theoretic context the method of dimensional regularization and minimal subtraction has been proposed, in [tHV72]. To the level considered here it is discussed in standard textbooks [ZJ89, Ami84], There the explicit calculation of the -factors can also be found. The method has been applied directly to the polymer system in the continuous chain limit in [Dup86a], where different versions of the approach are compared,... 

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