1993/05/26 by J. E. Hetrick, James E. Hetrick · 33 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Casimir effect #Gauge group #Gauge theory #Hamiltonian lattice gauge theory #Introduction to gauge theory #Lattice gauge theory #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #hep-lat #hep-th
paper · pdf · doi:10.1142/s0217751x94001242
published in International Journal of Modern Physics A 09(18), 3153-3178 (World Scientific) · 32 pages, 3 figures uuencoded, Plain TeX
arxiv created 1993/05/26 · openalex publication_date 1994/07/20 · arxiv updated 2015/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
SU (N) gauge fields on a cylindrical space-time are canonically quantized via two routes revealing almost equivalent but different quantizations. After removal of all continuous gauge degrees of freedom, the canonical coordinate A µ (in the Cartan subalgebra [Formula: see text]) is quantized. The compact route, as in lattice gauge theory, quantizes the Wilson loop W, projecting out gauge-invariant wave functions on the group manifold G. After a Casimir energy related to the curvature of SU (N) is added to the compact spectrum, it is seen to be a subset of the noncompact spectrum. States of the two quantizations with corresponding energy are shifted relative to each other, such that the ground state on G, χ0 (W), is the first excited state Ψ 1 (Aµ) on [Formula: see text]. The ground state Ψ 0 (A µ ) does not appear in the character spectrum, as its lift is not globally defined on G. Implications for lattice gauge theory and the sum-over-maps representation of two-dimensional QCD are discussed.