2,591 research outputs found
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 arises linearly in the small length scale,
, characterizing the finite-size effects, and is suppressed by
. 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 , with 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 āretrospectively registeredā with the Australian New Zealand Clinical Trials RegistryMelanie Hayman, Peter Reaburn, Matthew Browne, Corneel Vandelanotte, Stephanie Alley and Camille E. Shor
Leaf phenology amplitude derived from MODIS NDVI and EVI: maps of leaf phenology synchrony for Mesoā and South America
The leaf phenology (i.e. the seasonality of leaf amount and leaf demography) of ecosystems can be characterized through the use of Earth observation data using a variety of different approaches. The most common approach is to derive time series of vegetation indices (VIs) which are related to the temporal evolution of FPAR, LAI and GPP or alternatively used to derive phenology metrics that quantify the growing season. The product presented here shows a map of average āamplitudeā (i.e. maximum minus minimum) of annual cycles observed in MODISāderived NDVI and EVI from 2000 to 2013 for Mesoā and South America. It is a robust determination of the amplitude of annual cycles of vegetation greenness derived from a LombāScargle spectral analysis of unevenly spaced data. VI time series preāprocessing was used to eliminate measurement outliers, and the outputs of the spectral analysis were screened for statistically significant annual signals. Amplitude maps provide an indication of net ecosystem phenology since the satellite observations integrate the greenness variations across the plant individuals within each pixel. The average amplitude values can be interpreted as indicating the degree to which the leaf life cycles of individual plants and species are synchronized. Areas without statistically significant annual variations in greenness may still consist of individuals that show a wellādefined annual leaf phenology. In such cases, the timing of the phenology events will vary strongly within the year between individuals. Alternatively, such areas may consist mainly of plants with leaf turnover strategies that maintain a constant canopy of leaves of different ages. Comparison with in situ observations confirms our interpretation of the average amplitude measure. VI amplitude interpreted as leaf life cycle synchrony can support model evaluation by informing on the likely leaf turn over rates and seasonal variation in ecosystem leaf age distribution
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