Non-commutative model of quark interactions V.V. Khruschov (Kurchatov Institute) The talk on the International Conference “New Trends in High-Energy Physics”, Alushta, September 3-10, 2011

Despite of all theoretical and experimental achievements of QCD the theory of strong interactions of color particles cannot be considered as complete At present a few problems exist which are not solved, for instance, the confinement problem of color particles Another interesting problem is the nature of quark masses, in particular, the formation of the constituent quark masses The nonperturbative QCD phenomena are characterized by one or two scales, which are probably universal Non-commutative model of quark interactions-1/12 Motivation

Non-commutative model of quark interactions-2/12 The commutation relations of a quantum field theory with three new fundamental constants

Non-commutative model of quark interactions-3/12 Eight dimensional phase space

Non-commutative model of quark interactions-4/12 O(2,6) symmetry

Non-commutative model of quark interactions-5/12 New Dirac type equation

Non-commutative model of quark interactions-6/12 Non-commutative Klein-Gordon type equation

Non-commutative model of quark interactions-7/12 Interactions with gauge fields

Non-commutative model of quark interactions-8/12 Uncertainty of the transverse quark momentum

Non-commutative model of quark interactions-9/12 Constituent quark mass

Non-commutative model of quark interactions-10/12 Quark masses and  c, c values

Thank you for your attention ! Non-commutative model of quark interactions