Anomalous magnetic moment of anyons

Abstract

The anomalous magnetic moment of anyons is calculated to leading order in a 1/N expansion. It is shown that the gyromagnetic ratio g remains 2 to the leading order in 1/N . This result strongly supports that obtained in [2], namely that g=2 is in fact exact. 1

Planar supersymmetric quantum mechanics of a charged particle in an external electromagnetic field

“…where K ′ (φ,φ) is the superpotential given by the redefined Kähler prepotential of Eq. (38), now in terms of the chiral and antichiral superfield coordinates of the particle, φ andφ:…”

Anomalous magnetic moment in parity-conserving QED3

“…Before closing this section we would like to contrast this result on the anomalous magnetic moment within a large-N treatment of our parity invariant QED 3 -like model, with a corresponding computation in an anyonic model in three-dimensions [21]. There, the authors using again a spectral representation of the photon propagator, obtain the anomalous magnetic moment to leading order in 1/N for their model, which is different from ours in that it consists only of a single Abelian gauge field interacting with 2N + 1 fermion species, in the presence of an Abelian Chern-Simons (CS) term for the gauge field, with a coefficient κ.…”

“…In such a case, with intrinsic parity violation due to the dynamical CS term, the anomalous magnetic moment is essentially determined by the parity-violating parts of the dynamical gauge boson propagator, which are absent in our parity conserving case. The important thing the authors of [21] find is that, in the limit where the coefficient κ of the CS term is very large, the induced corrections to the magnetic moment are of order 1/mκ, where m is the bare fermion mass in their model. In fact, the result of the large-N computation of [21] indicates a quantum corrected magnetic moment µ = 1 m ( 1 2 + 1 κ ), which, with S = 1 2 + 1 κ identified as the spin of the anyon field [22], implies an exact (to leading order in 1/N) gyromagnetic ratio g = 2 for anyons.…”

“…The important thing the authors of [21] find is that, in the limit where the coefficient κ of the CS term is very large, the induced corrections to the magnetic moment are of order 1/mκ, where m is the bare fermion mass in their model. In fact, the result of the large-N computation of [21] indicates a quantum corrected magnetic moment µ = 1 m ( 1 2 + 1 κ ), which, with S = 1 2 + 1 κ identified as the spin of the anyon field [22], implies an exact (to leading order in 1/N) gyromagnetic ratio g = 2 for anyons. This result is in agreement with general arguments [22] that the gyromagnetic ratio of an anyon system should remain 2 to all orders in a quantum treatment of localised anyon fields.…”

Anomalous magnetic moment of anyons in three dimensional CP−1 model

“…Chou et al showed that the g-factor of nonrelativistic anyonic particles is exactly two [6]. Also, in field theoretical models, it is shown that in the pure anyonic limit (namely for large value of the coefficient of the Chern-Simons term) the gyromagnetic ratio of anyon at one-loop is g = 2 + O 1 κ where κ is the coefficient of the Chern-Simons term [7,8].…”