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ReceivedIt is presented the general method that allows to formulate 4D SU(N)Yang -Mills theory in terms of only local gauge invariant v ariables. For the case N=2, that is discussed in details, this gauge invariant formulation appears to be very similar to R 2 -gravity. 1.Introduction.In previous author's works it was given formulation of three dimensional SU(2) Yang -Mills (YM) theory in terms of local gauge invariant v ariables both at classical [1], [2] and quantum levels [15] a . I t w as found that obtained formulation is very similar to 3D Einstein gravity. Using analogy with gravity, i t w as discovered new static solution of classical four dimensional YM equations with singularity on the nite sphere that is analog of Schwarzschild solution in general relativity and represents connement potential for quantum particle moving inside this sphere.In this paper we will give generalization of these results for 4D case and SU(N) gauge group for arbitrary N. As in 3D case we will nd that in proposed gauge invariant v ariables YM theory seems very similar to gravity but, in contrast to 3D case, to R 2 -gravity rather than Einstein one. This analogy with gravity w as already exploited to obtained new interesting solutions of coupled Einstein -Yang -MillsHiggs equations [16].Gauge invariant formulation of three dimensional SU(2) YM theory presented # e-mail address: lunev@hep.phys.msu.su a It is necessary to note that similar constructionfor selfdual sector of 4D Euclidean YM theory was given in works [21]

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Simple bosonic path integral representation for path ordered exponent is derived. This representation is used, at first, to obtain new variant of non-Abelian Stokes theorem. Then new pure bosonic worldline path integral representations for fermionic determinant and Green functions are presented. Finally, applying stationary phase method, we get quasiclassical equations of motion in QCD. * electronic address: lunev@hep.phys.msu.su