arXiv subjects

J. Scott Little

Publications and source records attributed to J. Scott Little.

3 recordsLinked to original sources

arXiv2006

The Projection Operator Method and the Ashtekar-Horowitz-Boulware Model

Motivated by the recent work of Louko and Molgado, we consider the Ashtekar-Horowitz-Boulware model using the projection operator formalism. This paper uses the techniques developed in a recent paper of Klauder and Little to overcome the potential difficulties of this particular model. We also extend the model by including a larger class of functions than previously considered and evaluate the classical limit of the model.

gr-qc↗

arXiv2006

Highly Irregular Quantum Constraints

Motivated by a recent paper of Louko and Molgado, we consider a simple system with a single classical constraint R(q)=0. If q_l denotes a generic solution to R(q)=0, our examples include cases where R'(q_l)\ne 0 (regular constraint) and R'(q_l)=0 (irregular constraint) of varying order as well as the case where R(q)=0 for an interval, such as a \leq q \leq b. Quantization of irregular constraints is normally not considered; however, using the projection operator formalism we provide a satisfactory quantization which reduces to the constrained classical system when \hbar \to 0. It is noteworthy that irregular constraints change the observable aspects of a theory as compared to strictly regular constraints.

gr-qc↗

arXiv2005

Elementary Model of Constraint Quantization with an Anomaly

Quantum gravity is made more difficult in part by its constraint structure. The constraints are classically first-class; however, upon quantization they become partially second-class. To study such behavior, we focus on a simple problem with finitely many degrees of freedom and demonstrate how the projection operator formalism for dealing with quantum constraints is well suited to this type of example.

gr-qc↗