NVp x 2 h F2aj3 x t x1 x 2 t2 J dxdx 2dt2dx3dttfa x1 x 2 h

xVr (x3, t3 )F3aPr (x'^ x1''1;x2'^x3' t3)> (2-4.l5)

where F0, F1a, F2ap, Fjap,, are the power functionals of the zero, first, second, third, etc. powers, respectively.

The expansion Sln 0[n]^na(x, t) is the functional power series, the n-th term of which is determined by the form of the correlation tensor of (n +1)-th rank:

Sln 0[n]/<na(x, t) = -J dx1dttfp((1, t1 )Dap(x, t; x1, t1)

+ J dx1dt1dx2dt2Vp(*1, t1 )nY (x2, t2 Dp (x, t; x1, t1; x2, t2) + ... (2.4.16)

Substituting Eq. 2.4.15 and Eq. 2.4.16 in Eq. 2.4.12 we equate the functionals of the same power in the left and right hand parts of Eq. 2.4.12 to each other. The resultant infinite chain of connected equations is

'(¥ + L° t; X1' 1X2' t2 ) = -DaY (x't; X1' ^ x2 ' t2 )LrFo (x't )

- iDay (x, t; X1' t1 )LrF1p(( t; x 2, t2 ) - iD^ (x 't; x 2' t2 ))F1a(x't; x1' t1

+ 3iLrF3aPr (x't; x1' t1;x 2' t2; x 3' t3 )' J, (2.4.17)

'(¥ + L° t; X1' 1X2' t2 ) = -DaY (x't; X1' ^ x2 ' t2 )LrFo (x't )

- iDay (x, t; X1' t1 )LrF1p(( t; x 2, t2 ) - iD^ (x 't; x 2' t2 ))F1a(x't; x1' t1

+ 3iLrF3aPr (x't; x1' t1;x 2' t2; x 3' t3 )' J, (2.4.17)

In writing Eq. 2.4.16 we took into account that it was necessary to carry out a symmetrization over the arguments and indices of the factors na(x,t ) in the highest terms of the expansions described by Eq. 2.4.15 and Eq. 2.4.16. Assuming that one of the functionals Fn is equal to zero we shall obtain a closed set of equations. In particular, assuming F2 = Owe obtain from Eq. 2.4.17 the following set of equations:

(it + Lo j Fla (x, t; xi, ti) = -iDaj3(x, t; xi, ti )LpFo (x, t). (2.4.19)

To solve the set of Eq. 2.4.i8 and Eq. 2.4.i9, we introduce the functions pa(x,t;xi,ti) according to the relation

Fia(x, t; xi, ti ) = exp(- Lot )a(x, t; xi, ti). (2.4.20)

The action of the operator exp(- L0t) on an arbitrary function of coordinates and moments is, as it known, the substitution of r - Ar(() for r and p - Ap(() for p, where Ar(() and Ap(() are the variations of the radius-vector and momentum of a particle in the regular field during the time t. Substituting Eq. 2.4.20 in Eq. 2.4.i3, we shall obtain t

Fia(x,t;xi,ti)= -iJdt'exp(-Lo(t - t'))Da/l(x,t;xi,ti)o(x,t). (2.4.2i)

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