Aharanov Bohm Effect for Neutral Particles

Classical and Quantum Interaction of the Dipole

Jeeva Anandan

PRL 85, 1354-1357 (2000)

URL: http://prola.aps.org/abstract/PRL/v85/i7/p1354_1


In this paper, Anandan derives a relativistic Lagrangian for a neutral particle interacting with an electromagnetic field. The particle interacts via its electric and magnetic dipole moments. Anandan derives covariant expressions for the Lagrangian, velocity, and forces on the particle that take advantage the duality of the electric and magnetic dipoles.

There are two main results derived in this paper:
• A neutral particle has its own analog of the Aharanov-Bohm effect. The dipole moment (the sum of the electric and magnetic dipoles) leads to a Yang-Mills field strength and a topological phase, just like a gauge potential for charged particles.
• At low energies, the dipole moment enters the Hamiltonian in exactly the same way that the gauge potential enters the Hamiltonian of a charged particle.

When Anandan calculates the forces on a neutral particle with dipole moments, he finds several new terms in the forces acting on the particle in its rest frame. He concludes by proposing some experiments that would demonstrate the Aharanov Bohm effect for neutral particles.

I really enjoyed the derivation of the relativistic Lagrangian. I've not seen quantum mechanics derived from a covariant Lagrangian --- only quantum field theories. The relativistic Lagrangian would fit right into the machinery of path integrals. Perhaps there's no real benefit in treating the problem this way --- maybe you would just end up with the same forces Anandan arrived at by his Hamiltonian methods. Still, it saves you the trouble of quantizing the theory.

I found this paper when I came across a letter to the editor by Ivezic: http://link.aps.org/abstract/PRL/v98/e108901.

Ivezic's main point seems to be that Anandan should have used the 4-velocity dx/d(tau) instead of dx/dt. I don't see any major differences, although Ivezic claims his work "significantly influences" the low-energy Lagrangian. Strangely, he does not show what the corrections to Anandan's expressions are. That would have been useful.