Classical and quantal nonrelativistic Chern-Simons theory

Path-integral Fujikawa’s approach to anomalous virial theorems and equations of state for systems with SO(2,1) symmetry

“…Therefore, the equations derived here also apply in the case of inverse square potentials in arbitrary spatial dimension and other SO(2, 1) invariant systems such as anyons [37][38][39][40][41][42].…”

Some exact Bradlow vortex solutions

“…The Jackiw-Pi equation comes about naturally in some non-relativistic Chern-Simons theories [4,5,7], whereas the Popov equation describes vortices on a 2-sphere that are realized as Yang-Mills instantons on a manifold S 2 × H 2 (the vortices here are situated on the 2-sphere, whereas in Witten's solution they are situated on the hyperbolic plane). In a recent paper, Manton considered extending the vortex equations to nine different types -five of which can possess vortices -and thereby found two new ones [8]; one of them was dubbed the Bradlow equation and the other remained an unnamed equation.…”

“…Other vortex equations of similar type to Taubes equation are the Jackiw-Pi equation [4,5] and the Popov equation [6]; both of which possess exact analytic solutions and again on manifolds of constant Gaussian curvature. The Jackiw-Pi equation comes about naturally in some non-relativistic Chern-Simons theories [4,5,7], whereas the Popov equation describes vortices on a 2-sphere that are realized as Yang-Mills instantons on a manifold S 2 × H 2 (the vortices here are situated on the 2-sphere, whereas in Witten's solution they are situated on the hyperbolic plane).…”

Abelian Chern-Simons field theory and the anyon equation on a torus

“…Many particle quantum mechanics on the torus is also constructed [16][17][18][19] from the abelian Chern-Simons field theory like in the infinite plane case [21,22], and it is demonstrated that the degeneracy structure of the vacuum can affect the quantum mechanics and give rise to a multi-component anyon wavefunction [18][19][20]. It seems, however, that at least two essential points, quantization and periodic property of the matter field, are to be clarified.…”