2. Quasi-Classical Model in SU(N) Gauge Field Theory A.V.KOSHELKIN Moscow Institute for Physics and Engineering

3. CONTENTS 1. Introduction. 2. Statement of Problem and Main Goal. 3. Self-Consistent Solution. 4. Fermion and Gauge Field in Developed Model. 5. Application to QCD. 6. Conclusion.

4. PEOPLE C.N.Yang, R.L.Mills, Rev. 51 461 (1954). S.Coleman. Phys. Lett. B 70 59 (1977). T.Eguchi. Phys. Rev. D 13 1561 (1976). P.Sikivie, N.Weiss, Phys. Rev. 20 487 (1979). R.Jackiw, L.Jacobs, C.Rebbi, Phys. Rev. D21 426 (1980 ). R.Teh, W.K.Koo, C.H.Oh, Phys. Rev. D24 2305 (1981) V.M.Vyas,T.S.Raju, T.Shreecharan. e-Print: arXiv:0912.3993[het-th]. D.D.Dietrich, Phys Rev. D 80 (2009) 067701. A.Slavnov, L.Faddeev, Introduction to Quantum Theory of Gauage Fields, 2nd enl. and rev. ed. Moscow, Nauka, 1988. E.S.Fradkin, Nucl.Phys. 76 (1966) 588. and so on, so on … 1. Introduction.

5. 2.Statement of Problem and Main Goal.

6. Key Approximations The main goals are 1) to obtained such solutions that both the Yang-Mills and Dirac Equation would be satisfied together; 2) to quantize the fields; 3) to apply the obtained results to QCD.

7. The Yang-Mills equation WE ASSUME

8. The Dirac equation Provided that

9. SOLUTION IS (Koshelkin,Phys.Lett.,B683 (2010) 205)

10. 3. Self-Consistent Solution. a) Gauge field b) Fermion field

11. c) Relation equations The problem is solvable when the dimension of the gauge group. Thereat, the currents generated by fermions and gauge field exactly compensate each other. (Koshelkin,Phys.Lett.,B696 (2011) 539)

12. 4. Fermion and Gauge Field in Developed Model. In terms of the multi particle problem, the solutions correspond to individual states of particles the solutions correspond to collective states (Fermi liquid-like)

13. Fermion effective mass. IN EQUILIBRIUM 1) 2)

14. . 5. Application to QCD

18. 6.Final remarks and conclusion. 1.The self-consistent solutions of the non-homogeneous YM equation and the Dirac equation in the external YM field is derived in the quasi-classical model when the YM field is assumed to be in form of the eikonal wave. 2. The quantum theory of the considered model is developed in the quasi-classical approximation. 3. The considered model is solvable when the dimension of the gauge group and assumes that the fermion and gauge fields have to exist together. That is an alternative to Glasma model by L.D.McLerran and R.Venugopalan. 4. The relation of the developed model to the generally accepted point of view on the matter generated in collisions of heavy ions of high energies is considered. 5. The fermion and gauge fields derived in the explicit form allow to develop diagram technique beyond perturbative consideration.