Vacuum Force and Confinement

This is the authors' abstract. We don't add key points for this paper.

We show that confinement of quarks and gluons can be explained by their interaction with the vacuum Abelian gauge field A_vac, which is implicitly introduced by the canonical commutation relations and generates the vacuum force. The background gauge field A_vac, linear in coordinates of R³, is inherently present in quantum mechanics: it is introduced during the canonical quantization of phase space (T^*R³, ω ) of a nonrelativistic particle, when a potential θ of the symplectic 2-form ω =dθ on T^*R³ is mapped into a connection A_vac=-iθ on a complex line bundle L_v over T^*R³ with gauge group U(1)_v and curvature F_vac=d A_vac=-iω. Generalizing this correspondence to the relativistic phase space T^*R3,1, we extend the Dirac equation from R3,1 to T^*R3,1 while maintaining the condition that fermions depend only on x3,1. The generalized Dirac equation contains the interaction of fermions with A_vac and has particle-like solutions localized in space. Thus, the wave-particle duality can be explained by turning on or off the interaction with the vacuum field A_vac. Accordingly, confinement of quarks and gluons can be explained by the fact that their interaction with A_vac is always on and therefore they can only exist in bound states in the form of hadrons.