in SU(N) Gauge Field Theory The Non-Perturbative Self-Consistent Model in SU(N) Gauge Field Theory A.V.KOSHELKIN Moscow Institute for Physics and Engineering HCP'11, 14-18 November 2011, Paris, France

1.Statement of Problem and Main Goal HCP'11, 14-18 November 2011, Paris, France

HCP'11, 14-18 November 2011, Paris, France 2.Key Approximations 3.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 . HCP'11, 14-18 November 2011, Paris, France

HCP'11, 14-18 November 2011, Paris, France 4.RESULTS OF SOLUTIONS i) The Yang-Mills equation ANSATZ HCP'11, 14-18 November 2011, Paris, France

HCP'11, 14-18 November 2011, Paris, France ii) The Dirac equation _______________________________________________________________________________________________________________ ____________________________________________________________________________________________________ HCP'11, 14-18 November 2011, Paris, France

HCP'11, 14-18 November 2011, Paris, France

5. Self-Consistent Solution a) Gauge field b) Fermion field HCP'11, 14-18 November 2011, Paris, France

HCP'11, 14-18 November 2011, Paris, France c) Relation equations The problem is solvable when the dimension of the gauge group . In this way, the currents generated by fermions and gauge field exactly compensate each other. HCP'11, 14-18 November 2011, Paris, France

HCP'11, 14-18 November 2011, Paris, France Quantizing the Yang-Mills field HCP'11, 14-18 November 2011, Paris, France

6. 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) HCP'11, 14-18 November 2011, Paris, France

Fermion effective mass. EQUILIBRIUM 1) 2) HCP'11, 14-18 November 2011, Paris, France

HCP'11, 14-18 November 2011, Paris, France . 7. Application to QCD HCP'11, 14-18 November 2011, Paris, France

HCP'11, 14-18 November 2011, Paris, France

HCP'11, 14-18 November 2011, Paris, France

HCP'11, 14-18 November 2011, Paris, France

HCP'11, 14-18 November 2011, Paris, France 8.Final remarks and conclusion 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. HCP'11, 14-18 November 2011, Paris, France