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

Correlations around an interface

We compute one-loop correlation functions for the fluctuations of an interface using a field theory model. We obtain them from Feynman diagrams drawn with a propagator which is the inverse of the Hamiltonian of a Poschl-Teller problem. We derive an expression for the propagator in terms of elementary functions, show that it corresponds to the usual spectral sum, and use it to calculate quantities such as the surface tension and interface profile in two and three spatial dimensions. The three-dimensional quantities are rederived in a simple, unified manner, whereas those in two dimensions extend the existing literature, and are applicable to thin films. In addition, we compute the one-loop self-energy, which may be extracted from experiment, or from Monte Carlo simulations. Our results may be applied in various scenarios, which include fluctuations around topological defects in cosmology, supersymmetric domain walls, Z(N) bubbles in QCD, domain walls in magnetic systems, interfaces separating Bose-Einstein condensates, and interfaces in binary liquid mixtures.Comment: RevTeX, 13 pages, 6 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