Vacuum Force and Confinement
- URL: http://arxiv.org/abs/2402.06404v2
- Date: Mon, 19 Feb 2024 08:32:45 GMT
- Title: Vacuum Force and Confinement
- Authors: Alexander D. Popov
- Abstract summary: We show that confinement of quarks and gluons can be explained by their interaction with the vacuum Abelian gauge field $A_sfvac$.
- Score: 65.268245109828
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We show that confinement of quarks and gluons can be explained by their
interaction with the vacuum Abelian gauge field $A_{\sf{vac}}$, which is
implicitly introduced by the canonical commutation relations and generates the
vacuum force. The background gauge field $A_{\sf{vac}}$, linear in coordinates
of $\mathbb{R}^3$, is inherently present in quantum mechanics: it is introduced
during the canonical quantization of phase space $(T^*\mathbb{R}^3, \omega )$
of a nonrelativistic particle, when a potential $\theta$ of the symplectic
2-form $\omega =\mathrm{d}\theta$ on $T^*\mathbb{R}^3$ is mapped into a
connection $A_{\sf{vac}}=-\mathrm{i}\theta$ on a complex line bundle
$L_{\sf{v}}$ over $T^*\mathbb{R}^3$ with gauge group U(1)$_{\sf{v}}$ and
curvature $F_{\sf{vac}}=\mathrm{d} A_{\sf{vac}}=-\mathrm{i}\omega$.
Generalizing this correspondence to the relativistic phase space
$T^*\mathbb{R}^{3,1}$, we extend the Dirac equation from $\mathbb{R}^{3,1}$ to
$T^*\mathbb{R}^{3,1}$ while maintaining the condition that fermions depend only
on $x\in\mathbb{R}^{3,1}$. The generalized Dirac equation contains the
interaction of fermions with $A_{\sf{vac}}$ 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 $A_{\sf{vac}}$. Accordingly,
confinement of quarks and gluons can be explained by the fact that their
interaction with $A_{\sf{vac}}$ is always on and therefore they can only exist
in bound states in the form of hadrons.
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