Year: 1994
Type: article
Abstract: Since the gauge group underlying (2+1)-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately choosing the measure that features in the definition of the loop transform. Thus, `old-fashioned' loop representations---based on ordinary loops---do exist. In the case when the spatial topology is that of a 2-torus, these can be constructed explicitly; all quantum states can be represented as functions of (homotopy classes of) loops and the scalar product and the action of the basic observables can be given directly in terms of loops.
Source: Classical and Quantum Gravity
Authors: Abhay Ashtekar, R Loll
Institution: Pennsylvania State University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2047303640