Quantum statistical correlations in thermal field theories: boundary effective theory

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field $\phi_c$, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schr\"{o}dinger field-representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle-point for fixed boundary fields, which is the classical field $\phi_c$, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally-reduced effective theory for the thermal system. We calculate the two-point correlation as an example.Comment: 13 pages, 1 figur

Dissipative quantum systems modeled by a two level reservoir coupling

The coupling between a quantum dynamical system and a two-level system reservoir is analysed within the framework of the Feynman-Vernon theory. We stress the differences between this new reservoir and the well-known bath of oscillators and show that, in order to obtain the Langevin equation for the system of interest in the high temperature regime, we have to choose a spectral distribution function $J(\omega)$ which is finite for $\omega=0$.Comment: 6 pages, RevteX, preprint UNICAM

Pressure of massless hot scalar theory in the boundary effective theory framework

We use the boundary effective theory (BET) approach to thermal field theory in order to calculate the pressure of a system of massless scalar fields with quartic interaction. The method naturally separates the infrared physics, and is essentially non-perturbative. To lowest order, the main ingredient is the solution of the free Euler-Lagrange equation with non-trivial (time) boundary conditions. We derive a resummed pressure, which is in good agreement with recent calculations found in the literature, following a very direct and compact procedure.Comment: 10 pages, 4 figure

Challenging inequity in mathematics education by making pedagogy more visible to learners

This paper reports on initial findings from the Visible Maths Pedagogy research project, a collaboration between an academic researcher and two teacher researchers (the paper’s authors). The aim of the project was to explore the effects of making pedagogy more visible on students’ success in school mathematics. We adopted a Participatory Action Research methodology to plan and evaluate five strategies used alongside ‘progressive’ teaching approaches to make the teacher’s pedagogical rationale more visible to learners. Our findings show that students, particularly those from disadvantaged backgrounds, were initially prone to misinterpret the intentions of the teacher. However, the five strategies helped students gain a greater appreciation of the teacher’s pedagogical rationale and how to respond appropriately. We discuss the implications of these findings for enabling all students to access the benefits of progressive teaching approaches and for opening up to scrutiny what it means to be a successful learner of mathematics

Visible mathematics pedagogy: A model for transforming classroom practice

This paper focuses on the development of a model of research and professional development which aims to bring about transformations in classroom practice in situations that have previously proved resistant to change. We explore reasons why conventional models have failed to address one such situation, the continuing predominance of teacher-centred pedagogies in mathematics classrooms. We draw on findings from the Visible Mathematics Pedagogy research project to highlight how a critical model of participatory action research can be refined to enhance its potential to bring about changes in classroom practice. We report on research tools and processes that were developed, distinct from those commonly used in research, including the organisation of research team meetings around participatory principles, the active involvement of teachers in designing and employing data collection tools, and in generating protocols associated with video-stimulated reflection. We demonstrate how these research tools and processes enhanced collaboration and teacher agency, the trustworthiness of the research findings and teachers’ critical reflection on existing practice. We argue that our refined model of participatory action research can inform and support teachers and researchers wishing to transform classroom practice, especially in situations analogous to many mathematics classrooms, in which conventional models have had limited impact

Economic Reforms and Human Development: Evidence from Transition Economies

Do market-oriented economic reforms result in higher levels of human well-being? This article studies the impact of macro-level institutional and infrastructure reforms on the economic, educational and health dimensions of human well-being among 25 transition economies. We use panel data econometrics based on the LSDVC technique to analyse the effects of market-oriented reforms on the human development index (HDI), as a measure of human well-being, from 1992 to 2007. The results show the complexity of reform impacts in transition countries. They show that institutional and economic reforms led to positive economic effect and significant impacts on other dimensions of human development. We find some positive economic impacts from infrastructure sectors reforms. However, not every reform measure appears to generate positive impacts. Large-scale privatizations show negative effects in health and economic outcomes. The overall results show the importance of the interaction among different reform measures and the combined effect of these on human development