The Edge states of the BF system and the London equations
May, 199238 pages
Published in:
- Int.J.Mod.Phys.A 8 (1993) 723-752
e-Print:
- hep-th/9205116 [hep-th]
Report number:
- SU-4240-507
Citations per year
Abstract:
It is known that the 3d Chern-Simons interaction describes the scaling limit of a quantum Hall system and predicts edge currents in a sample with boundary, the currents generating a chiral Kac-Moody algebra. It is no doubt also recognized that in a somewhat similar way, the 4d interaction (with a two form, the dual of the eletromagnetic current, and F the electromagnetic field form) describes the scaling limit of a superconductor. We show in this paper that there are edge excitations in this model as well for manifolds with boundaries. They are the modes of a scalar field with invariance under the group of diffeomorphisms (diffeos) of the bounding spatial two-manifold. Not all of this group seem implementable by operators in quantum theory, the implementable group being a subgroup of volume preserving diffeos. The system in this manner can lead to the algebra and its variants. Lagrangians for fields on the bounding manifold which account for the edge observables on quantization are also presented. They are the analogues of the dimentional massless scalar field Lagrangian describing the edge modes of an abelian Chern-Simons theory with a disk as the spatial manifold. We argue that the addition of ``Maxwell'' terms constructed from and do not affect the edge states, and that the augmented Lagrangian has an infinite number of conserved charges- the aforementioned scalar field modes- localized at the edges. This Lagrangian is known to describe London equations and a massive vector field. A dimensional generalization of the Hall effect involving vortices coupled to is also proposed.Note:
- 38 pages
- gauge field theory: U(1)
- gauge field theory: tensor
- dimension: 3
- Hall effect
- quantization
- Hamiltonian formalism
- model: superconductivity
- superconductivity: model
- algebra: Kac-Moody
- algebra: W(infinity)
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