Renormalization schemes choice

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. 

In this framework, we present the repercussions on the physical properties of a renormalized indirect correlation function y (r) conjugated with an optimized division scheme. All the units are expressed in terms of the LJ parameters, that is, reduced temperature T = kBT/e and reduced density p = pa3. In order to examine the consequences of a renormalization scheme, the direct correlation function c(r) calculated from ZSEP conjugated with DHH splitting is compared in Fig. 7 to those obtained with the WCA separation. For high densities, the differences arise mainly in the core region for y(r) and c(r) [77]. These calculated quantities are in excellent agreement with simulation data. The reader has to note that similar results have been obtained with the ODS scheme (see Ref [80]). Since the acuracy of c(r) can be affected by the choice of a division scheme, the isothermal compressibility is affected too, as can be seen in Table III for the pkBTxT quantity. As compared to the values obtained with... 

Once the choice of basis functions for the irreducible representations of Dto has been made, the 3-J symbols can be calculated as integrals analogously to the 3-/ symbols (Sect. 4). Therefore, they may also be calculated from the corresponding 3-1 symbols of R3 using a positive constant of renormalization. The scheme for direct multiplication of the irreducible representations of D[Pg.232]

Different types of the MMCC(2,3), MMCC(2,4), and MMCC(3,4) approximations are obtained by making different choices for o) in eqs (35)-(37) (7,16-18). The most intriguing results are obtained when wave functions o) are defined by the low-order MBPT. The MBPT-like forms of o) lead to the renormcdized and completely renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) schemes (7,16-18). As demonstrated below, these new methods represent powerful computational tools that remove the failing of the standard CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approximations at large internuclefu separations, while preserving the simplicity and black-box character of the noniterative perturbative CC approaches. 

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