An algebraic extension of Dirac quantization: Examples

An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of non-linear, diffeomorphism invariant theories such as general relativity. Recently, an extension of the required type was proposed by one of us using algebraic quantization methods. In this paper, the key conceptual and technical aspects of the algebraic program are illustrated through a number of finite dimensional examples. The choice of examples and some of the analysis is motivated by certain peculiar problems endemic to quantum gravity. However, prior knowledge of general relativity is not assumed in the main discussion. Indeed, the methods introduced and conclusions arrived at are applicable to any system with first class constraints. In particular, they resolve certain technical issues which are present also in the reduced phase space approach to quantization of these systems.Comment: 43 pages, Latex, CGPG-94/6-1. (References added; particularly to earlier work by C.J.Isham using group theoretic ideas, in the introduction.

Minisuperspaces: Observables and Quantization

A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit expressions of Dirac observables, i.e.\ phase space functions which commute weakly with the constraint. This, in turn, enables us to carry out a general quantization program to completion. We are also able to address the issue of time through ``deparametrization'' and discuss physical questions such as the fate of initial singularities in the quantum theory. We find that they persist in the quantum theory {\it inspite of the fact that the evolution is implemented by a 1-parameter family of unitary transformations}. Finally, certain of these models admit conditional symmetries which are explicit already prior to the canonical transformation. These can be used to pass to quantum theory following an independent avenue. The two quantum theories --based, respectively, on Dirac observables in the new canonical variables and conditional symmetries in the original ADM variables-- are compared and shown to be equivalent.Comment: 34 page

Evaluation and demonstration of a propellant quantity gaging system for auxiliary propulsion systems Final report

Bipropellant quantity gaging digital syste

An algebraic approach to the quantization of cosntrained systems: finite dimensional examples

From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate non-canonical variables. In this dissertation I consider an algebraic formulation of the Dirac approach to the quantization of constrained systems, due to A. Ashtekar. The Dirac quantization program is augmented by a general principle to find the inner product on physical states. Essentially, the Hermiticity conditions on physical operators determine this inner product. I also clarify the role in quantum theory of possible algebraic identities between the elementary variables. I use this approach to quantize various finite dimensional systems. Some of these models test the new aspects of the algebraic framework. Others bear qualitative similarities to \gr, and may give some insight into the pitfalls lurking in \qg. In (spatially compact) general relativity, the Hamiltonian is constrained to vanish. I present various approaches one can take to obtain an interpretation of the quantum theory of such ``dynamically constrained'' systems. I apply some of these ideas to the Bianchi I cosmology, and analyze the issue of the initial singularity in quantum theory.Comment: 124 pages, LaTeX (run twice before printing), SU-GP-92/8-1. (Minor corruption (extra blank line at line 2994) hopefully fixed.

Cognitive Behavioral Therapy with a Depressed Outpatient: Assessing Change in Cognitive Distortions as Measured by the Inventory of Cognitive Distortions

This single subject case study was conducted to determine the usefulness of a new measure, the Inventory of Cognitive Distortions (lCD). The main purpose was to determine the effectiveness of the ICD in noting changes in dysfunctional thinking during cognitive behavioral therapy. Because of the high incidence of depression in the population, a subject diagnosed with Major Depressive Disorder was determined to be the most appropriate choice for assessing the effectiveness of this measure in the clinical setting. The cognitive behavioral treatment implemented was a manualized approach using Gilson and Freeman\u27s (1999), Overcoming Depression. This treatment was a collaborative effort between the individual and the therapist; the individual using the manual for homework assignments and for reinforcement of what was learned in the therapeutic sessions. From baseline to termination the patient attended a total of 10 sessions, with a follow-up approximately one month later. Assessment involved clinical interviews, Multimodal Life History Inventory (Lazarus & Lazarus, 1991), the Structured Clinical Interview for DSM-IV Axis I Disorders (SCID I; First, M.B., Spitzer, R.L., Gibbon, M., & Williams, J.B.W., 1997), the Beck Depression Inventory (BDI; Beck, Steer & Brown, 1996) the Beck Anxiety Inventory (BAI; Beck, Epstein, Brown & Steer, 1988), and the Beck Hopelessness Scale (BHS; Beck, Weissman, Lester, Trexler, 1974), the Inventory of Cognitive Distortions (lCD: Yurica & DiTomasso, 2002), and the Dysfunctional Attitude Scale (DAS; Beck & Weissman, 1978; Weissman, 1979). The ICD and the DAS were used at baseline, at termination, and at follow-up to note any changes (or cessation) in dysfunctional thinking throughout treatment. The research findings indicated reductions in self-report scores as the client and therapist worked through the manualized treatment. Homework was an important component. Three self reports (BDI,BAI, BHS) were completed for each session. Reading and working on the manual and the chapter exercises was essential; other homework varied according to the individual\u27s needs. Those included completion of a Daily Thought Record (DTR) to determine patterns and/or triggers in distorted thinking. Because the client seemed to struggle with passive-aggressive tendencies she used writing as a vehicle to express her feelings calmly; she learned and practiced, in session, the assertiveness skills which were to be used beyond the therapeutic setting. The results indicated that cognitive behavioral therapy, in a manualized format, was effective in reducing depressive symptoms and that the lCD was able to indicate changes in the distorted thinking of the subject, as hypothesized

Remember the Titans, Historical Fact or Fiction?

In the late 1990s, screen writer Gregory A. Howard wrote a screen play called Remember the Titans, based on the true story of T.C. Williams High School in Alexandria, Virginia. Jerry Bruckheimer and Walt Disney Pictures bought the script based on the fact that it is a true story, but much of the film‟s content is fictional. Gregory Howard admitted to ESPN writer Jeff Merron that “he made some big assumptions when writing his script” (qtd. in Merron 5). Though the film is not entirely historically accurate, it is successful because it appeals to Americans through its intense emotional drama, its powerful music and its strong characterization