The Kramers equation simulation algorithm II. An application to the Gross-Neveu model

We continue the investigation on the applications of the Kramers equation to the numerical simulation of field theoretic models. In a previous paper we have described the theory and proposed various algorithms. Here, we compare the simplest of them with the Hybrid Monte Carlo algorithm studying the two-dimensional lattice Gross-Neveu model. We used a Symanzik improved action with dynamical Wilson fermions. Both the algorithms allow for the determination of the critical mass. Their performances in the definite phase simulations are comparable with the Hybrid Monte Carlo. For the two methods, the numerical values of the measured quantities agree within the errors and are compatible with the theoretical predictions; moreover, the Kramers algorithm is safer from the point of view of the numerical precision.Comment: 20 pages + 1 PostScript figure not included, REVTeX 3.0, IFUP-TH-2

Exact calculation of the radiatively-induced Lorentz and CPT violation in QED

Radiative corrections arising from the axial coupling of charged fermions to a constant vector b_\mu can induce a Lorentz- and CPT-violating Chern-Simons term in the QED action. We calculate the exact one-loop correction to this term keeping the full b_\mu dependence, and show that in the physically interesting cases it coincides with the lowest-order result. The effect of regularization and renormalization and the implications of the result are briefly discussed.Comment: LaTex, 8 pages; minor correction

Evaluating Summer Flounder Spatial Sex-Segregation in a Southern New England Estuary

Marine fish species can exhibit sex-specific differences in their biological traits. Not accounting for these characteristics in the stock assessment or management of a species can lead to misunderstanding its population dynamics and result in ineffective regulatory strategies. Summer Flounder Paralichthys dentatus, a flatfish that supports significant commercial and recreational fisheries along the northeastern U.S. shelf, expresses variation in several traits between the sexes, including growth and habitat preference. To further understand these patterns, 1,302 Summer Flounder were collected and sexed in 2016 and 2017 from fisheries-independent surveys conducted in Rhode Island state waters. Female flounder were more prevalent in shallow waters (15 m) from May through September. The probability of a collected flounder being female was evaluated with generalized linear models and covariates representing depth, temperature, month, year, and TL. Summer Flounder were more likely to be female at larger sizes, in shallower waters, and late in the season. When compared with landings data in the recreational fishery over the sampling period, the results suggest that nearly all flounder harvested in the sector were female. This work provides further evidence for and characterization of Summer Flounder sex-segregation and highlights, for management purposes, the importance of considering fine-scale spatial dynamics in addition to broader distribution patterns. The fitted model represents an effective first step toward understanding the implications of an aggregated fishing effort for disproportionate removals of male or female flounder and for exploring resulting consequences for regional spawning stock biomass and stock resiliency

Local Casimir Energy For Solitons

Direct calculation of the one-loop contributions to the energy density of bosonic and supersymmetric phi-to-the-fourth kinks exhibits: (1) Local mode regularization. Requiring the mode density in the kink and the trivial sectors to be equal at each point in space yields the anomalous part of the energy density. (2) Phase space factorization. A striking position-momentum factorization for reflectionless potentials gives the non-anomalous energy density a simple relation to that for the bound state. For the supersymmetric kink, our expression for the energy density (both the anomalous and non-anomalous parts) agrees with the published central charge density, whose anomalous part we also compute directly by point-splitting regularization. Finally we show that, for a scalar field with arbitrary scalar background potential in one space dimension, point-splitting regularization implies local mode regularization of the Casimir energy density.Comment: 18 pages. Numerous new clarifications and additions, of which the most important may be the direct derivation of local mode regularization from point-splitting regularization for the bosonic kink in 1+1 dimension

Inhibition of EZH2 Ameliorates Lupusâ Like Disease in MRL/lpr Mice

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151823/1/art40931_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151823/2/art40931.pd

Three-dimensional N=4 supersymmetry in harmonic N=3 superspace

We consider the map of three-dimensional N=4 superfields to N=3 harmonic superspace. The left and right representations of the N=4 superconformal group are constructed on N=3 analytic superfields. These representations are convenient for the description of N=4 superconformal couplings of the Abelian gauge superfields with hypermultiplets. We analyze the N=4 invariance in the non-Abelian N=3 Yang-Mills theory.Comment: Latex file, 22 pages; v2 two references adde

The coupling of fermions to the three-dimensional noncommutative CPN−1CP^{N-1} model: minimal and supersymmetric extensions

We consider the coupling of fermions to the three-dimensional noncommutative $CP^{N-1}$ model. In the case of minimal coupling, although the infrared behavior of the gauge sector is improved, there are dangerous (quadratic) infrared divergences in the corrections to the two point vertex function of the scalar field. However, using superfield techniques we prove that the supersymmetric version of this model with ``antisymmetrized'' coupling of the Lagrange multiplier field is renormalizable up to the first order in $\frac{1}{N}$. The auxiliary spinor gauge field acquires a nontrivial (nonlocal) dynamics with a generation of Maxwell and Chern-Simons noncommutative terms in the effective action. Up to the 1/N order all divergences are only logarithimic so that the model is free from nonintegrable infrared singularities.Comment: Minor corrections in the text and modifications in the list of reference

Mode regularization of the susy sphaleron and kink: zero modes and discrete gauge symmetry

To obtain the one-loop corrections to the mass of a kink by mode regularization, one may take one-half the result for the mass of a widely separated kink-antikink (or sphaleron) system, where the two bosonic zero modes count as two degrees of freedom, but the two fermionic zero modes as only one degree of freedom in the sums over modes. For a single kink, there is one bosonic zero mode degree of freedom, but it is necessary to average over four sets of fermionic boundary conditions in order (i) to preserve the fermionic Z$_2$ gauge invariance $\psi \to -\psi$, (ii) to satisfy the basic principle of mode regularization that the boundary conditions in the trivial and the kink sector should be the same, (iii) in order that the energy stored at the boundaries cancels and (iv) to avoid obtaining a finite, uniformly distributed energy which would violate cluster decomposition. The average number of fermionic zero-energy degrees of freedom in the presence of the kink is then indeed 1/2. For boundary conditions leading to only one fermionic zero-energy solution, the Z$_2$ gauge invariance identifies two seemingly distinct `vacua' as the same physical ground state, and the single fermionic zero-energy solution does not correspond to a degree of freedom. Other boundary conditions lead to two spatially separated $\omega \sim 0$ solutions, corresponding to one (spatially delocalized) degree of freedom. This nonlocality is consistent with the principle of cluster decomposition for correlators of observables.Comment: 32 pages, 5 figure

Central charge and renormalization in supersymmetric theories with vortices

Some quantum features of vortices in supersymmetric theories in 1+2 dimensions are studied in a manifestly supersymmetric setting of the superfield formalism. A close examination of the supercurrent that accommodates the central charge and super-Poincare charges in a supermultiplet reveals that there is no genuine quantum anomaly in the supertrace identity and in the supercharge algebra, with the central-charge operator given by the bare Fayet-Iliopoulos term alone. The central charge and the vortex spectrum undergo renormalization on taking the expectation value of the central-charge operator. It is shown that the vortex spectrum is exactly determined at one loop while the spectrum of the elementary excitations receives higher-order corrections.Comment: 9 pages, revte