1994/11/24 by A. P. Balachandran, A.P. BALACHANDRAN, L. Chandar +3 · 39 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary value problem #Curse of dimensionality #Gauge theory #Hamiltonian (control theory) #Higgs boson #Higgs field #Lattice gauge theory #Observable #Operator (biology) #Physical system #Quantum and Classical Electrodynamics #Topological Materials and Phenomena #cond-mat #hep-ph #hep-th
paper · pdf · doi:10.1142/s0217751x95000966
published in International Journal of Modern Physics A 10(13), 1969-1993 (World Scientific) · 36 pages, LATEX File (revised because figures had problems)
arxiv created 1994/11/24 · openalex publication_date 1995/05/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/08
Gauge theories on manifolds with spatial boundaries are studied. It is shown that observables localized at the boundaries (edge observables) can occur in such models irrespective of the dimensionality of space-time. The intimate connection of these observables to charge fractionation, vertex operators and topological field theories is described. The edge observables, however, may or may not exist as well-defined operators in a fully quantized theory depending on the boundary conditions imposed on the fields and their momenta. The latter are obtained by requiring the Hamiltonian of the theory to be self-adjoint and positive-definite. We show that these boundary conditions can also have nice physical interpretations in terms of certain experimental parameters, such as the penetration depth of the electromagnetic field in a surrounding superconducting medium. The dependence of the spectrum on one such parameter is explicitly exhibited for the Higgs model on a spatial disk in its London limit. It should be possible to test such dependences experimentally, the above Higgs model for example being a model for a superconductor. Boundary conditions for the (3+1)-dimensional BF system confined to a spatial ball are studied. Their physical meaning is clarified and their influence on the edge states of this system (known to exist under certain conditions) is discussed. It is pointed out that edge states occur for topological solitons of gauge theories such as the ’t Hooft-Polyakov monopoles.