- #1
Roberto Pavani
- 22
- 5
- TL;DR
- If QED correctly explains ##(g-2)\neq 0##, does this constitute indirect evidence that ##dF=0## everywhere; i.e. no magnetic monopole? Or does it only constrain the local region of the experiment?
While working on a preprint, I noticed what seems to be a straightforward logical chain that I haven't seen stated explicitly in the literature. I'd like to understand whether (a) it's well-known but considered too trivial to state, (b) it has been discussed somewhere, or (c) there's a flaw I'm missing.
The chain is:
1. The anomalous magnetic moment ##(g-2)_e/2## is measured to ##\sim 10^{-13}## precision.
2. Its value is reproduced by QED loop corrections involving the photon field ##A_\mu##.
3. The standard QED calculation assumes ##A_\mu## is a globally defined potential, so that ##F = dA##.
4. ##F = dA## implies ##dF = d^2A = 0## identically; i.e. ##\nabla\cdot\mathbf{B} = 0##: no magnetic monopole.
Now, the obvious objection: in Dirac's formulation (1931), monopoles and ##A_\mu## coexist
##A_\mu## is defined everywhere except on the Dirac string, and the Schwinger loop diagram presumably doesn't "see" a distant
monopole. So the chain might only say: "in the region where the electron interacts with the field, ##dF=0## holds".
This raises the question I'd like to understand:
- Has anyone computed what happens to ##(g-2)## in a theory that admits monopoles (Dirac quantisation, 't Hooft–Polyakov)? Would the agreement with experiment be spoiled, or would the correction be negligible for a distant monopole?
- If a monopole existed at distance ##R## from the experiment, at what ##R## would it start affecting the ##(g-2)## calculation?
- Is the ##10^{-13}## precision of ##(g-2)_e## actually constraining the monopole flux in some indirect way that direct searches (MoEDAL, MACRO) do not?
I'm not claiming anything new, just trying to understand whether this connection has been made explicit somewhere, or whether it's trivial / flawed.
References I've checked without finding an explicit statement:
- Schwinger (1948), original ##(g-2)## calculation
- Jackson, Classical Electrodynamics, Ch. 6 (monopoles)
- Preskill, "Magnetic Monopoles" (1984 review)
- Rajantie, "Introduction to Magnetic Monopoles" (2012)
Any pointers appreciated.
The chain is:
1. The anomalous magnetic moment ##(g-2)_e/2## is measured to ##\sim 10^{-13}## precision.
2. Its value is reproduced by QED loop corrections involving the photon field ##A_\mu##.
3. The standard QED calculation assumes ##A_\mu## is a globally defined potential, so that ##F = dA##.
4. ##F = dA## implies ##dF = d^2A = 0## identically; i.e. ##\nabla\cdot\mathbf{B} = 0##: no magnetic monopole.
Now, the obvious objection: in Dirac's formulation (1931), monopoles and ##A_\mu## coexist
##A_\mu## is defined everywhere except on the Dirac string, and the Schwinger loop diagram presumably doesn't "see" a distant
monopole. So the chain might only say: "in the region where the electron interacts with the field, ##dF=0## holds".
This raises the question I'd like to understand:
- Has anyone computed what happens to ##(g-2)## in a theory that admits monopoles (Dirac quantisation, 't Hooft–Polyakov)? Would the agreement with experiment be spoiled, or would the correction be negligible for a distant monopole?
- If a monopole existed at distance ##R## from the experiment, at what ##R## would it start affecting the ##(g-2)## calculation?
- Is the ##10^{-13}## precision of ##(g-2)_e## actually constraining the monopole flux in some indirect way that direct searches (MoEDAL, MACRO) do not?
I'm not claiming anything new, just trying to understand whether this connection has been made explicit somewhere, or whether it's trivial / flawed.
References I've checked without finding an explicit statement:
- Schwinger (1948), original ##(g-2)## calculation
- Jackson, Classical Electrodynamics, Ch. 6 (monopoles)
- Preskill, "Magnetic Monopoles" (1984 review)
- Rajantie, "Introduction to Magnetic Monopoles" (2012)
Any pointers appreciated.