Automatic Computation of Feynman Diagrams

Quantum corrections significantly influence the quantities observed in modern particle physics. The corresponding theoretical computations are usually quite lengthy which makes their automation mandatory. This review reports on the current status of automatic calculation of Feynman diagrams in particle physics. The most important theoretical techniques are introduced and their usefulness is demonstrated with the help of simple examples. A survey over frequently used programs and packages is provided, discussing their abilities and fields of applications. Subsequently, some powerful packages which have already been applied to important physical problems are described in more detail. The review closes with the discussion of a few typical applications for the automated computation of Feynman diagrams, addressing current physical questions like properties of the $Z$ and Higgs boson, four-loop corrections to renormalization group functions and two-loop electroweak corrections.Comment: Latex, 62 pages. Typos corrected, references updated and some comments added. Vertical offset changed. The complete paper is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ttp98/ttp98-41/ or via www at http://www-ttp.physik.uni-karlsruhe.de/Preprints

An Investigation of Students' Learning of Integral Calculus with Maple Software and Paper-Pencil Strategies in the Western Region of Ghana.

The goal of the research was to look into the impact of Maple software instruction on senior high school students' understanding of integral calculus. The study adopted a mixed-method design comprising qualitative and quantitative research designs. The researcher used both purposive and simple random sampling techniques to select one hundred (100) participants: fifty (50) participants for the control group and fifty (50) participants for the experimental group. The data collection instruments used in the study were an interview, pre-test and post-test. Data analysis was carried out using descriptive statistics and an Independent Samples t-test. The study found that 7(7%) participants found it difficult to execute correct substitution of the lower and upper limits of definite integral questions. Moreover, most of the participants, 35(35%), omitted the constant of integration after responding to the indefinite integral test item of the pre-test. It was noted that 18(18%) of the participants could not correctly integrate the polynomial or quadratic function administered to them. The independent samples t-test analysis of the post-test scores for the experimental and control groups revealed a statistically significant difference between the experimental group (M = 24.80; SD = 9.48) and the control group (M = 20.65; SD = 7.67). The estimated t-statistic was (t = 2.986; p = 0.005). This shows that Maple Software's experimental group outperformed the control group using the paper and pencil strategy. The analysis of the interview data indicated that Maple Software has contributed to the success of students’ achievement in the integral calculus by arousing and sustaining the student’s interest. The Maple Software also made it easier for students to follow the calculus instruction. The findings recommended that technology and mathematical software should be used in the teaching and learning of integration at schools

Integrated technologies instructional method to enhance bilingual undergraduate engineering students

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonMathematics permeates almost every aspect of human life and it is a skill much needed by the increasingly complex technological world. It is necessary that this essential skill must be properly developed among students to prepare them for future academic and professional careers. An assessment of the research-based instructional strategies blending with old traditional methods with the modern technological development is a must. Due to the complexity of mathematics learning and the varied learning styles of learners, an integration of appropriate multiple instructional strategies into mathematics education will positively impact mathematical achievement of students. The purpose of this research was to examine the effects of the use of Integrated Technologies Instructional Method (ITIM) as a supplement to the traditional lecture method on mathematics achievement of the Integral Calculus students at the College of Engineering, University of Ha'il, Saudi Arabia. The ITIM includes the four instructional strategies such as the use of the Computer-Supported Collaborative Learning, the collaborative learning, the bilingual support and the study support. Different types of academic supports have been used to examine their effects on students achievement in mathematics. Mathematics, the bedrock of science and engineering, is considered a very important indicator of a student's academic success in professional higher education. Undergraduate engineering students' low achievement in the first year mathematics is an issue demands much attention. The study was undertaken to address students' weak background in mathematics and particularly their high failure rates in this particular course. A total of 218 undergraduate engineering students, comprising of both the experimental and the control groups, were involved in this experimental design study. The control group was taught by the traditional lecture method whereas the experimental group was exposed to the ITIM as a supplement to the traditional lecture method. Apart from the effects of the use of ITIM, students' performance in the previous courses (covariates) such as mathematics, computer, and the English language were compared with their final grades of the Integral Calculus course. The final grades of students were taken as the dependent variable and the ITIM and students' scores in the previous courses as the independent variables. It has been noticed from the literature review that the application of only one instructional strategy does not address the needs of the diverse learning styles of students. A mixed mode method, quantitative and qualitative, was used to collect and analyse data. The quantitative data instruments included students' final exam grades and the student questionnaires. Interviews with students were used as qualitative tools of data collection. An independent t-test, ANOVA, univariate analysis and the stepwise multiple regression analysis were performed to determine the overall statistical significance. The study concluded that there was a statistically significant difference in the performance of the experimental group of students' in terms of their end-of-course grades compared to that of the control group. The regression model revealed significance of covariates on the dependent variable. However, no significant relationship was found between the mathematics achievement and attitudes towards the use of ITIM. The study was an attempt to demonstrate the suitability of the instructional strategies on the bilingual Arab undergraduate engineering students; however, they can probably be applicable to other bilingual students

Dynamical Mean-Field Theory within the Full-Potential Methods: Electronic structure of Ce-115 materials

We implemented the charge self-consistent combination of Density Functional Theory and Dynamical Mean Field Theory (DMFT) in two full-potential methods, the Augmented Plane Wave and the Linear Muffin-Tin Orbital methods. We categorize the commonly used projection methods in terms of the causality of the resulting DMFT equations and the amount of partial spectral weight retained. The detailed flow of the Dynamical Mean Field algorithm is described, including the computation of response functions such as transport coefficients. We discuss the implementation of the impurity solvers based on hybridization expansion and an analytic continuation method for self-energy. We also derive the formalism for the bold continuous time quantum Monte Carlo method. We test our method on a classic problem in strongly correlated physics, the isostructural transition in Ce metal. We apply our method to the class of heavy fermion materials CeIrIn_5, CeCoIn_5 and CeRhIn_5 and show that the Ce 4f electrons are more localized in CeRhIn_5 than in the other two, a result corroborated by experiment. We show that CeIrIn_5 is the most itinerant and has a very anisotropic hybridization, pointing mostly towards the out-of-plane In atoms. In CeRhIn_5 we stabilized the antiferromagnetic DMFT solution below 3K, in close agreement with the experimental N\'eel temperature.Comment: The implementation of Bold-CTQMC added and some test of the method adde

Estimating the two-particle KK-matrix for multiple partial waves and decay channels from finite-volume energies

An implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the L\"uscher formalism and involving a Hermitian matrix known as the "box matrix" is described. The method includes higher partial waves and multiple decay channels. Two fitting procedures for estimating the $K$-matrix parameters, which properly incorporate all statistical covariances, are discussed. Formulas and software for handling total spins up to $S=2$ and orbital angular momenta up to $L=6$ are obtained for total momenta in several directions. First tests involving $\rho$-meson decay to two pions include the $L=3$ and $L=5$ partial waves, and the contributions from these higher waves are found to be negligible in the elastic energy range.Comment: 32 pages, 1 figur