The Concept of Electric Charge and the Hypothesis of Magnetic Poles

Abstract

We examine a generic field theory in which the field particle has two couplings. It is of particular interest when these are the electroweak, e, and the hypothetical magnetoweak, g. The new field operators are obtained by replacing the field operators $\Psi (x)$ of the standard model or of similar models by $\tilde{\Psi} (x) D^j_q (m,m')$ where $ D^j_q (m,m')$ is an element of the $2j+1$ dimensional representation of the SLq(2) algebra, which is also the knot algebra. The field is assumed to exist in two phases distinguished by two values of $q$: $q_e = \frac{e}{g}$ and $q_g = \frac{g}{e}$ which label the electroweak and magnetoweak phases respectively. We assume that the observed leptons and quarks are composed of e-preons and are in agreement with the observed charge spectrum of leptons and quarks. It is now proposed that there is also a g-phase where g-leptons and g-quarks are composed of g-preons. It is assumed that the g-charge is very large compared to the e-charge and the mass of the g charged particle is even larger since the mass of all of these particles is partially determined by the eigenvalues of $\bar{D}^j_q (m,m') D_q^j (m,m')$, a polynomial in $q$, that multiplies the Higgs mass term and where \begin{equation*} \frac{q_g}{q_e} = \left ( \frac{\hbar c}{e^2} \right)^2 \approx (137)^2. \end{equation*} These values of $q$ indicate that particles in the g-phase are much more massive, they should be harder to produce or to observe.