Abstract
We use the manifestly Lorentz covariant canonical formalism to evaluate eigenvalues of the area operator acting on Wilson lines. To this end we modify the standard definition of the loop states to make it applicable to the present case of noncommutative connections. The area operator is diagonalized by using the usual shift ambiguity in the definition of the connection. The eigenvalues are then expressed through quadratic Casimir operators. No dependence on the Immirzi parameter appears.
- Received 30 March 2001
DOI:https://doi.org/10.1103/PhysRevD.64.044023
©2001 American Physical Society