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**Example text**

2,3,12]. Their explicit form is irrelevant for what follows. 74) into them. 76) 1R H(x ) (x )2 >(x )2"0 . S. Ya. Palchik / Physics Reports 300 (1998) 1—111 In virtue of Eq. 87) with i"1, 2, the condition of vanishing of the fields R H can be written in the I form dy dy CI J 2 Q (x y y )1 j (y ) (y ) (x )2 >(x )2"0 . 77) will hereinafter be referred to as the irreducibility condition of the conformal current, or the condition of absence of the electromagnetic interaction. Note that Eq. 77) select out the class of theories in which all the Green functions of the current are uniquely determined by the ¼ard identities; see also Section 6 for details.

X ), k"2, 2, 2n. As an example we display its expression for I s"1: L (x ) (x ) I I . I I#2d x x I I IL> I Next section contains expressions in more complicated cases. S. Ya. Palchik / Physics Reports 300 (1998) 1—111 The Green functions of the fields P2 are defined by Eq. 150) upon the substitution Q "(d#s, s). The functions CI N entering Eq. 150) are orthogonal to the functions CN , see I IJ IJ Eq. 151), and can be represented in the form (see Refs. [3,6,15] for more details) CI N "CI J 2 Q(x x x )"1 J 2 Q(x ) J (x )hI (x )2 IJ IJI I I I IJ 2 jV BJ (x x x ) , "jV BJ 2 Q(x x x )#jV BJ 2 Q(x x x )!

S. Ya. Palchik / Physics Reports 300 (1998) 1—111 51 may be also found. 1. The corresponding Ward identities also have anoQY malous contributions of these fields. In Section 4 we give the examples of such anomalous Ward identities. 1 . 18) I Q I V Q\K K The analogous terms enter the commutator [j (x), PH(y)]. The HK QK operators in Eq. 1 . The j derivatives act on the argument of a field P2 (y) only. y) (jW)Q\K>P, r"0, 1, 2, m , V which, in principle, could be calculated for any class of models.