Phase structure of Causal Dynamical Triangulations in 4D

Causal Dynamical Triangulations (CDT) is a lattice approach to quantum gravity. CDT has rich phase structure, including a semiclassical phase consistent with Einstein's general relativity. Some of the observed phase transitions are second (or higher) order which opens a possibility of investigating the ultraviolet continuum limit. Recently a new phase with intriguing geometric properties has been discovered and the new phase transition is also second (or higher) order.Comment: To appear in Acta Physica Polonica B Proceedings Supplement. Presented at the 3rd Conference of the Polish Society on Relativity. 5 pages, 1 figur

Beliefs and Technology - Does One Lead to the Other? Evaluating the Effects of Teacher Self-Efficacy and School Collective Efficacy on Technology Use in the Classroom

This exploratory mixed method study builds upon previous research to investigate the influence of teacher self- and collective efficacy on technology use in the classroom. This population was purposefully sampled to examine first- and second order technology barriers, instructional strategies, and human influences on technology. The quantitative finding was supported by qualitative analysis of the teacher interviews and led to the conclusion that even thought there were strong teacher tendencies towards a belief in using technology actual practice demonstrated a lack of productivity or transference of that belief into classroom practice. A high self- and collective efficacy had no effect on technology use in the classroom and a belief in technology did not lead to the use of technology. The study explored three research questions: 1) what is the effect of teacher self-efficacy on technology use in the classroom, 2) what is the effect of collective efficacy on technology use in the classroom, and 3) what is the relationship among teacher self-efficacy, collective efficacy, and barriers that inhibit technology use in a K-12 classroom setting? Thirty-five teachers in a New Jersey K-8 school district volunteered to take a 36-question survey. Three teachers were interviewed to corroborate the survey data. This study is unique in the combined analysis of self- and collective efficacy and technology. It raises several questions for future study. Teacher responses overwhelmingly identified first order or extrinsic barriers as impediments to technology. These included poor technical support, access, time issues, and a lack of vision and training. These barriers are decades old and have been acknowledged for as long as technology has been in the classroom. Why, despite thirty years of technology in education, do the same barriers that existed in the very beginning continue to be strong deterrents of technology use? Teachers identified administrators as the least influential on teacher practices. If this is so, how can there be such a high sense of collective efficacy? How much influence does the collective agency have on classroom teacher behavior? Specifically, at what point in a teacher\u27s decision-making does the collective agency over-ride personal beliefs and what are the characteristics that contribute to this conflict and possible submissive behavior? Finally, are we seeking answers to the wrong questions? Is it possible that teachers and educational systems are not able to modify intrinsic and standard operating practices to utilize technology successfully

Some of my Journal Entries During COVID-19

These are some journal entries that I was looking back on while we were sent home in quarantine. They began during the period of time when the coronavirus first seemed to effect my life. I believe they are able to show some of the ways God was working amidst the uncertainty

Searching for a continuum limit in causal dynamical triangulation quantum gravity

We search for a continuum limit in the causal dynamical triangulation (CDT) approach to quantum gravity by determining the change in lattice spacing using two independent methods. The two methods yield similar results that may indicate how to tune the relevant couplings in the theory in order to take a continuum limit.Comment: 19 pages, 8 figures. Title change and journal reference adde

Pseudo-Cartesian coordinates in a model of Causal Dynamical Triangulations

Causal Dynamical Triangulations is a non-perturbative quantum gravity model, defined with a lattice cut-off. The model can be viewed as defined with a proper time but with no reference to any three-dimensional spatial background geometry. It has four phases, depending on the parameters (the coupling constants) of the model. The particularly interesting behavior is observed in the so-called de Sitter phase, where the spatial three-volume distribution as a function of proper time has a semi-classical behavior which can be obtained from an effective mini-superspace action. In the case of the three-sphere spatial topology, it has been difficult to extend the effective semi-classical description in terms of proper time and spatial three-volume to include genuine spatial coordinates, partially because of the background independence inherent in the model. However, if the spatial topology is that of a three-torus, it is possible to define a number of new observables that might serve as spatial coordinates as well as new observables related to the winding numbers of the three-dimensional torus. The present paper outlines how to define the observables, and how they can be used in numerical simulations of the model.Comment: 26 pages, 15 figure

Causal Dynamical Triangulations on a torus

Causal Dynamical Triangulations (CDT) is a non-perturbative lattice approach to quantum gravity where one assumes space-time foliation into spatial hyper-surfaces of fixed topology. Most of the previous studies of CDT were done for the fixed spatial topology of the 3-sphere. We present recent results for the fixed spatial topology of the 3-torus. We argue that the topology change does neither affect the phase structure nor the order of the phase transitions. Thus, the CDT properties seem to be universal, independently of the spatial topology choice

Quantum gravity on a torus

Causal Dynamical Triangulations (CDT) is a non-perturbative lattice approach to quantum gravity where one assumes space-time foliation into spatial hyper-surfaces of fixed topology. Most of the CDT results were obtained for the spatial topology of the 3-sphere. It was shown that CDT has rich phase structure, including the semiclassical phase consistent with Einstein's general relativity. Some of the phase transitions were found to be second (or higher) order which makes a possibility of taking continuum limit viable. Here we present new results of changing the spatial topology to that of the 3-torus. We argue that the topology change does not change the phase structure nor the order of the phase transitions. Therefore CDT results seem to be universal independent of the topology chosen.Comment: To appear in Acta Physica Polonica B Proceedings Supplement. Presented at the 6th Conference of the Polish Society on Relativity. 4 pages, 1 figur

New higher-order transition in causal dynamical triangulations

We reinvestigate the recently discovered bifurcation phase transition in Causal Dynamical Triangulations (CDT) and provide further evidence that it is a higher order transition. We also investigate the impact of introducing matter in the form of massless scalar fields to CDT. We discuss the impact of scalar fields on the measured spatial volumes and fluctuation profiles in addition to analysing how the scalar fields influence the position of the bifurcation transition.Comment: 15 pages, 11 figures. Conforms with version accepted for publication in Phys. Rev.