Analysis of the Lee-Yang zeros in a dynamical mass generation model in three dimensions

We investigate a strongly U(1) gauge theory with fermions and scalars on a three dimensional lattice and analyze whether the cintinuum limit might be a renormalizable theory with dynamical mass generation. Most attention is paid to the weak coupling region where a possible new dynamical mass generation mechanism might exist. There we investigate the mass of the composite fermion, the chiral condensate and the scaling of the Lee-Yang zeros.Comment: 3 pages,4 figures,talk presented at Lattice97(Edinburgh

The Causal Interpretation of Quantum Mechanics and The Singularity Problem in Quantum Cosmology

We apply the causal interpretation of quantum mechanics to homogeneous quantum cosmology and show that the quantum theory is independent of any time-gauge choice and there is no issue of time. We exemplify this result by studying a particular minisuperspace model where the quantum potential driven by a prescribed quantum state prevents the formation of the classical singularity, independently on the choice of the lapse function. This means that the fast-slow-time gauge conjecture is irrelevant within the framework of the causal interpretation of quantum cosmology.Comment: 18 pages, LaTe

Universal transloader moves delicate equipment without stress

Transloader moves delicate or heavy items over irregular surfaces without transmitting stress to the load. The loader is supported on three pivot points which produce a wrap free base. The base is supported by an artificial four-wheel frame

Translated Poisson approximation to equilibrium distributions of Markov population processes

The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in Kolmogorov distance, is of the smallest order that is compatible with their having integer support. Here, an approximation in the much stronger total variation norm is established, without any loss in the asymptotic order of accuracy; the approximating distribution is a translated Poisson distribution having the same variance and (almost) the same mean. Our arguments are based on the Stein-Chen method and Dynkin's formula.Comment: 18 page

Strongly coupled lattice gauge theory with dynamical fermion mass generation in three dimensions

We investigate the critical behaviour of a three-dimensional lattice \chiU\phi_3 model in the chiral limit. The model consists of a staggered fermion field, a U(1) gauge field (with coupling parameter $\beta$) and a complex scalar field (with hopping parameter $\kappa$). Two different methods are used: 1) fits of the chiral condensate and the mass of the neutral unconfined composite fermion to an equation of state and 2) finite size scaling investigations of the Lee-Yang zeros of the partition function in the complex fermion mass plane. For strong gauge coupling ($\beta < 1$) the critical exponents for the chiral phase transition are determined. We find strong indications that the chiral phase transition is in one universality class in this $\beta$ interval: that of the three-dimensional Gross-Neveu model with two fermions. Thus the continuum limit of the \chiU\phi_3 model defines here a nonperturbatively renormalizable gauge theory with dynamical mass generation. At weak gauge coupling and small $\kappa$, we explore a region in which the mass in the neutral fermion channel is large but the chiral condensate on finite lattices very small. If it does not vanish in the infinite volume limit, then a continuum limit with massive unconfined fermion might be possible in this region, too.Comment: 27 pages, 16 figure

Einstein gravity as a 3D conformally invariant theory

We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is irrelevant. The dual theory is invariant under foliation preserving 3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume (for the spatially compact case). Locally, this symmetry is identical to that of Horava-Lifshitz gravity in the high energy limit but our theory is equivalent to Einstein gravity. Specifically, we find that the solutions of general relativity, in a gauge where the spatial hypersurfaces have constant mean extrinsic curvature, can be mapped to solutions of a particular gauge fixing of the dual theory. Moreover, this duality is not accidental. We provide a general geometric picture for our procedure that allows us to trade foliation invariance for conformal invariance. The dual theory provides a new proposal for the theory space of quantum gravity.Comment: 27 pages. Published version (minor changes and corrections

Quenched QCD at finite density

Simulations of quenched $QCD$ at relatively small but {\it nonzero} chemical potential $\mu$ on $32 \times 16^3$ lattices indicate that the nucleon screening mass decreases linearly as $\mu$ increases predicting a critical chemical potential of one third the nucleon mass, $m_N/3$, by extrapolation. The meson spectrum does not change as $\mu$ increases over the same range, from zero to $m_\pi/2$. Past studies of quenched lattice QCD have suggested that there is phase transition at $\mu = m_\pi/2$. We provide alternative explanations for these results, and find a number of technical reasons why standard lattice simulation techniques suffer from greatly enhanced fluctuations and finite size effects for $\mu$ ranging from $m_\pi/2$ to $m_N/3$. We find evidence for such problems in our simulations, and suggest that they can be surmounted by improved measurement techniques.Comment: 23 pages, Revte

A longitudinal study of fat mass accrual from adolescence through to emerging adulthood and its impact on cardiometabolic risk later in life

Overweight and obesity (OWO), specifically abdominal obesity, are linked with cardiovascular and metabolic disease risk (CMR) at every stage of life. The prevalence of OWO nearly doubles in Canadians between childhood/adolescence and adulthood, suggesting that normal weight (NW) status is not stable through the life course and that there is a period in adulthood when fat mass (FM) increases. Emerging adulthood (EA; 18-25 years) has been identified as a potential critical period when FM accrues, the degree to which is potentially influenced by childhood and adolescence FM accrual. EA is also a period which favors trunk fat depots and when CMR likely commences or increases from child and adolescent levels. However, there is a paucity of longitudinal data describing the patterns and predictors of FM accrual during EA. Furthermore, there is also a lack of information showing how EA fat mass trajectories relate to adult cardiometabolic health. Thus, the primary purpose of this thesis is to describe patterns and predictors of total body fat (TBF) and trunk fat (TrF) mass accrual and OWO status in EA. The second purpose is to identify if trajectories of FM accrual in EA influence later adult CMR. The thesis will also explore sex differences. In study 1, 126 participants (59 male) were drawn from the Pediatric Bone Mineral Accrual Study (PBMAS) (1991-2011). Participants of the PBMAS were aged 8 to 15 years at the initial measurement. Serial measures of participants included chronological age (CA), biological age (BA - years from peak height velocity (PHV)), body mass index (BMI), and percent total body fat (%TBF). Study 1 is divided into two papers - 1a and 1b. The results from paper 1a based on this study indicated that fat mass increased from PHV into EA. At PHV, 9% of males and 14% of females were OWO by BMI, rising to 65% and 32%, respectively, 15 years after PHV (approximately 27 years in females, and 29 years in males). The prevalence of OWO by %TBF, increased from 29% to 45% in males, and from 33% to 59% in females over the same period. Differences in values of %TBF and BMI at PHV between those identified as NW had disappeared by 19-22 years (p>0.05) (i.e. fat mass between NW and OWO youth became more similar with age). OWO status at PHV did not predict OWO status during EA (p<0.05). These results indicate that EA appears to be a major period of transition from NW to OWO status. In addition, sex and FM metrics showed differences in ages when NW individuals became OWO. Study 1 also attempted to address the potential discrepancy in OWO identification and age at onset of OWO by different metrics in paper 1b, using the same PBMAS cohort. Longitudinal measures, including anthropometrics and dual x-ray absorptiometry from 1991-2017 were used to create hierarchical random effects models. Coefficients from the models were then used to develop growth curves, and these were compared to known cut-points. The age at onset of OWO was considered that age at which the predicted line crossed metric specific cut-offs. Age at onset of OWO in males was identified as 23.5 years by BMI and 21.5 years for % fat mass (%FM). Waist circumference (WC) cut-offs for OWO classification were not reached by 39 years. In females, onset was at 22.5 years by BMI, 15 years by %FM and 33.5 years by WC. Cut-points for BMI failed to identify 21.4% of OWO males and 56% of OWO females identified by %FM. The discrepancy in age at OWO between measures suggests that the most conservative indicator of age at onset is sex specific. BMI identifies OWO in males sooner than %FM. The opposite is true in females; however, BMI likely misses “over fatness” - more in females. WC may not be as appropriate for indicating risk in young adults and youth as in older adults. Using the same participants identified in study 1, study 2 created longitudinal models of fat accrual during EA and beyond (18 to 30 years of age) and identified concurrent and childhood/adolescent predictors of FM accrual, including measures of physical activity (PA) and energy intake (EI). It was found that childhood and adolescent TBF and TrF (0.30 ± 0.05, p<0.05) predicted EA accrual in both sexes and that concurrent PA (-0.06 ± 0.02, p<0.05) was significant in males only. These results underscored the importance of maintaining lower amounts of TBF and TrF mass during childhood and adolescence, and maintaining high level of PA in EA in order to mitigate TBF and TrF mass accrual and reduce the risk of transitioning from NW to OWO during EA. In study 3 (1991-2017) participants of the PBMAS, now aged 32 to 40 years of age, were invited back for reassessment. Blood analysis was used to create a Continuous Cardiometabolic Risk (conCMR) score for each participant. Multi-level models of TrF and TBF accrual were created looking at the same predictors as study 2, with the addition of cardiometabolic risk (CMR) group. Childhood TBF and TrF z-scores were again found to be the most significant predictor of TBF and TrF accrual, this time from 18-39 years. PA was also significant. CMR group did not influence the trajectory of TBF or TrF accrual, potentially due to the homogeneity of the group and the small sample size. In conclusion it was found that FM continues to increase steadily from late adolescence through EA leading to a marked increase in the prevalence of OWO in young adulthood. Greater trajectories during EA are related to higher levels of FM accrual in childhood and adolescence, and higher scores on individual CMR factors in later adulthood. The results suggest that maintaining high levels of PA throughout the life span is beneficial to adult health directly and through its mitigating effect on FM accrual in EA, and indirectly by limiting FM accumulation in childhood and adolescence

Scale-invariant gravity: Spacetime recovered

The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms and conformal transformations. Recently a manifestly 3-dimensional theory was constructed with conformal superspace as the configuration space. Here a fully 4-dimensional action is constructed so as to be invariant under conformal transformations of the 4-metric using general relativity as a guide. This action is then decomposed to a (3+1)-dimensional form and from this to its Jacobi form. The surprising thing is that the new theory turns out to be precisely the original 3-dimensional theory. The physical data is identified and used to find the physical representation of the theory. In this representation the theory is extremely similar to general relativity. The clarity of the 4-dimensional picture should prove very useful for comparing the theory with those aspects of general relativity which are usually treated in the 4-dimensional framework.Comment: Replaced with final version: minor changes to tex

Local limit approximations for Markov population processes

The paper is concerned with the equilibrium distribution $\Pi_n$ of the $n$-th element in a sequence of continuous-time density dependent Markov processes on the integers. Under a (2+\a)-th moment condition on the jump distributions, we establish a bound of order O(n^{-(\a+1)/2}\sqrt{\log n}) on the difference between the point probabilities of $\Pi_n$ and those of a translated Poisson distribution with the same variance. Except for the factor $\sqrt{\log n}$, the result is as good as could be obtained in the simpler setting of sums of independent integer-valued random variables. Our arguments are based on the Stein-Chen method and coupling.Comment: 19 page