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I'm trying to understand how magnetic monopoles and how its potential mirror and antiparticle counterparts would behave. So according to the modified lorentz force law $$\vec{F}=q_e\left(\vec{E}+\frac{\vec{v}}{c} \times \vec{B}\right)+q_m\left(\vec{B}-\frac{\vec{v}}{c} \times \vec{E}\right)$$

Say a moving magnetic monopole that is deflected counterclockwise by an electron would be deflected clockwise by an positron.

$$E=\pm \frac{e}{4\pi\epsilon_{0}r^{2}}\hat{r}$$ So with small test positive monopole moving to the right azimuthally $\vec{v}=v\hat{\phi}$ it will experience a force downwards in the positive polar direction.

$\vec{F}=\mp \frac{q_{m}e}{4\pi \epsilon_0 c r^2}\hat{\theta}$

So we should have a mirror counterpart with opposite parity that experiences a force in the upwards negative polar direction in the same electric field.

So would the antiparticle of the magnetic monopole also have its parity reversed? In that case it would behave the same around the electron/positron since the opposite charge and parities would cancel out?

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  • $\begingroup$ You need to tighten up this question. If the deflecting particles are stationary, then there is no magnetic field to cause the deflection, it's entirely electric. Unless you include the fact that charged fermions have magnetic fields from their magnetic moment. Then, making the deflecting particle have the same mass as the moving particle makes it hard to talk about in this context b/c recoil, so: use either massive spin-0 (anti)nucleus (real or hypothetical) vs a massive scalar N or S monopole. $\endgroup$
    – JEB
    Commented Mar 30 at 0:26
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    $\begingroup$ it would also help if you included a drawing of $A$ deflecting in the presence of $B$, maybe two version deflecting in opposite directions. $\endgroup$
    – JEB
    Commented Mar 30 at 0:31
  • $\begingroup$ Okay I've made the question more clear. I just mean a simple example of the force experienced by a moving magnetic monopole in the presence of a electron or positron in the center. $\endgroup$
    – CrazyDolphin
    Commented Mar 30 at 0:43
  • $\begingroup$ I'm confused by what you mean by "parity" here and what relation it has to the motion of a magnetic monopole here. In the sense that it's normally used in physics, it doesn't seem to be immediately relevant. (Charge conjugation would be more directly relevant but I don't know how a magnetic monopole would behave under that operation.) $\endgroup$
    – Michael Seifert
    Commented Mar 30 at 12:00
  • $\begingroup$ @MichaelSeifert I read that the magnetic monopole charge is a pseudoscalar and would change sign under parity transformation. So my two questions would basically be if there is a parity quantum number associsted with a magnetic monopole that changes how it would react in an electric field produced by a electron and positron as I wrote in my edited OP. And if anti monopole would have that parity inverted as well, so the anti monopole would behave the same in this situation and only the mirror of the anti monopole would behave differently. $\endgroup$
    – CrazyDolphin
    Commented Mar 30 at 14:57

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