Year: 1994
Type: conference-paper
Abstract: The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall effect. 2) Quantisation on multiply connected spaces and a topological proof the spin‐statistics theorem which avoids quantum field theory and relativity. Under 1), after explaining the meaning of gauge invariance and the theory of constraints, we discuss boundary conditions on gauge transformations and the definition of internal symmetries in gauge field theories. We then show how the edge states in the quantum Hall effect can be derived from the Chern‐Simons action using the preceding ideas. Under 2), after explaining the significance of fibre bundles for quantum physics, we review quantisation on multiply connected spaces in detail, explaining also mathematical ideas such as those of the universal covering space and the fundamental group. These ideas are then used to prove the aforementioned topological spin‐statistics theorem.
Source: AIP conference proceedings
DOI: 10.1063/1.46854
Author: A. P. Balachandran
Institution: Syracuse University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: U.S. Department of Energy
OpenAlex ID: W2123388065