Point-Particle Effective Field Theory III: Relativistic Fermions and the Dirac Equation

We formulate point-particle effective field theory (PPEFT) for relativistic spin-half fermions interacting with a massive, charged finite-sized source using a first-quantized effective field theory for the heavy compact object and a second-quantized language for the lighter fermion with which it interacts. This description shows how to determine the near-source boundary condition for the Dirac field in terms of the relevant physical properties of the source, and reduces to the standard choices in the limit of a point source. Using a first-quantized effective description is appropriate when the compact object is sufficiently heavy, and is simpler than (though equivalent to) the effective theory that treats the compact source in a second-quantized way. As an application we use the PPEFT to parameterize the leading energy shift for the bound energy levels due to finite-sized source effects in a model-independent way, allowing these effects to be fit in precision measurements. Besides capturing finite-source-size effects, the PPEFT treatment also efficiently captures how other short-distance source interactions can shift bound-state energy levels, such as due to vacuum polarization (through the Uehling potential) or strong interactions for Coulomb bound states of hadrons, or any hypothetical new short-range forces sourced by nuclei.Comment: 29 pages plus appendices, 3 figure

Point-Particle Effective Field Theory I: Classical Renormalization and the Inverse-Square Potential

Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original problem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective point-particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction {\em catalysis}, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.Comment: LaTeX, 20 pages plus appendi

Point-Particle Effective Field Theory II: Relativistic Effects and Coulomb/Inverse-Square Competition

We apply point-particle effective field theory (PPEFT) to compute the leading shifts due to finite-size source effects in the Coulomb bound energy levels of a relativistic spinless charged particle. This is the analogue for spinless electrons of the contribution of the charge-radius of the source to these levels, and we disagree with standard calculations in several ways. Most notably we find there are two effective interactions with the same dimension that contribute to leading order in the nuclear size. One is the standard charge-radius contribution, while the other is a contact interaction whose leading contribution to $\delta E$ arises linearly in the small length scale, $\epsilon$, characterizing the finite-size effects, and is suppressed by $(Z\alpha)^5$. We argue that standard calculations miss the contributions of this second operator because they err in their choice of boundary conditions at the source for the wave-function of the orbiting particle. PPEFT predicts how this boundary condition depends on the source's charge radius, as well as on the orbiting particle's mass. Its contribution turns out to be crucial if the charge radius satisfies $\epsilon \lesssim (Z\alpha)^2 a_B$, with $a_B$ the Bohr radius, since then relativistic effects become important. We show how the problem is equivalent to solving the Schr\"odinger equation with competing Coulomb, inverse-square and delta-function potentials, which we solve explicitly. A similar enhancement is not predicted for the hyperfine structure, due to its spin-dependence. We show how the charge-radius effectively runs due to classical renormalization effects, and why the resulting RG flow is central to predicting the size of the energy shifts. We discuss how this flow is relevant to systems having much larger-than-geometric cross sections, and the possible relevance to catalysis of reactions through scattering with monopoles.Comment: LaTeX, 22 pages plus appendices, v3: revised appendices, made more precise and concise discussion about proton radius for mesonic system

Feasibility, acceptability and efficacy of a web-based computer-tailored physical activity intervention for pregnant women - the Fit4Two randomised controlled trial

Background: Physical activity (PA) during pregnancy is associated with a variety of health benefits including a reduced risk of pregnancy related conditions such as pre-eclampsia and pregnancy-induced hypertension and leads to greater control over gestational weight gain. Despite these associated health benefits, very few pregnant women are sufficiently active. In an attempt to increase health outcomes, it is important to explore innovative ways to increase PA among pregnant women. Therefore, the aim of this study was to assess the feasibility, acceptability and efficacy of a four week web-based computer-tailored PA intervention among pregnant women. Methods: Seventy-seven participants were randomised into either: (1) an intervention group that received tailored PA advice and access to a resource library of articles relating to PA during pregnancy; or (2) a standard information group that only received access to the resources library. Objective moderate-to-vigorous physical activity (MVPA) was assessed at baseline and immediately post-intervention. Recruitment, attrition, intervention adherence, and website engagement were assessed. Questions on usability and satisfaction were administered post-intervention. Results: Feasibility was demonstrated through acceptable recruitment (8.5 participants recruited and randomised/ month), and attrition (25%). Acceptability among intervention group participants was positive with high intervention adherence (96% of 4 modules completed). High website engagement (participants logged in 1.6 times/week although only required to log in once per week), usability (75/100), and satisfaction outcomes were reported in both groups. However, participants in the intervention group viewed significantly more pages on the website (p < 0.05), reported that the website felt more personally relevant (p < 0.05), and significantly increased their MVPA from baseline to postintervention (mean difference = 35.87 min), compared to the control group (mean difference = 9.83 min) (p < 0.05), suggesting efficacy. Conclusions: The delivery of a computer-tailored web-based intervention designed to increase PA in pregnant women is feasible, well accepted and associated with increases in short-term MVPA. Findings suggest the use of computer-tailored information leads to greater website engagement, satisfaction and greater PA levels among pregnant women compared to a generic information only website. Trial registration: The trial was ‘retrospectively registered’ with the Australian New Zealand Clinical Trials RegistryMelanie Hayman, Peter Reaburn, Matthew Browne, Corneel Vandelanotte, Stephanie Alley and Camille E. Shor

Fabrication and mechanical testing of a new sandwich structure with carbon fiber network core

The aim is the fabrication and mechanical testing of sandwich structures including a new core material known as fiber network sandwich materials. As fabrication norms for such a material do not exist as such, so the primary goal is to reproduce successfully fiber network sandwich specimens. Enhanced vibration testing diagnoses the quality of the fabrication process. These sandwich materials possess low structural strength as proved by the static tests (compression, bending), but the vibration test results give high damping values, making the material suitable for vibro-acoustic applications where structural strength is of secondary importance e.g., internal panelling of a helicopter