Abstract
The nonperturbative quantization technique a la Heisenberg is applied for the SU(3) gauge theory. The operator Yang-Mills equation and corresponding infinite set of equations for all Green’s functions are considered. Gauge degrees of freedom are splitted into two groups: (1) A μ a ∈ SU (2) × U (1) ⊂ SU (3); (2) coset degrees of freedom SU (3)/SU (2) × U (1). Using some assumptions about 2- and 4-point Green’s functions, the infinite set of equations is truncated to two equations. The first equation is the SU (2) × U (1) Yang-Mills equation, and the second equation describes a gluon condensate formed by coset fields. A flux tube solution describing longitudinal color electric fields stretched between quark and antiquark located at the ± infinities is obtained. It is shown that the dual Meissner effect appears in this solution: the electric field is pushed out from the gluon condensate.
Highlights
One of the most important problems in modern physics is the problem of nonperturbative quantization
The problem is that force lines between a quark and an antiquark are confined into a flux tube and the field strength decreases exponentially with distance from quarks
This situation is fundamentally different from the situation with positive and negative charges in electrodynamics where the field strength decreases as a power law
Summary
One of the most important problems in modern physics is the problem of nonperturbative quantization. The problem is that force lines between a quark and an antiquark are confined into a flux tube and the field strength decreases exponentially with distance from quarks. This situation is fundamentally different from the situation with positive and negative charges in electrodynamics where the field strength decreases as a power law. Heisenberg offered the procedure of nonperturbative (NP) quantization for a nonlinear spinor field [1]. We apply Heisenberg’s idea to nonperturbative quantization of SU(3) gauge fields. This talk is based on [2]
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