Chiral symmetry restoration and axial vector renormalization for Wilson fermions

Lattice gauge theories with Wilson fermions break chiral symmetry. In the U(1) axial vector current this manifests itself in the anomaly. On the other hand it is generally expected that the axial vector flavour mixing current is non-anomalous. We give a short, but strict proof of this to all orders of perturbation theory, and show that chiral symmetry restauration implies a unique multiplicative renormalization constant for the current. This constant is determined entirely from an irrelevant operator in the Ward identity. The basic ingredients going into the proof are the lattice Ward identity, charge conjugation symmetry and the power counting theorem. We compute the renormalization constant to one loop order. It is largely independent of the particular lattice realization of the current.Comment: 11 pages, Latex2

A small caseid synapsid, Arisierpeton simplex gen. et sp. nov., from the early Permian of Oklahoma, with a discussion of synapsid diversity at the classic Richards Spur locality

The fossil record of caseids, a clade of faunivorous to large herbivorous Permian synapsids, is unusual in having a poorly documented history. Although Kungurian caseids are common in the well-known continental deposits of North America, and the fossil record of the group extends into the middle Permian (Guadalupian), with the presence of the large caseid Ennatosaurus in the Mezen Basin faunal assemblage, only two other occurrences are known in older Permian age sediments. One is an undescribed caseid from the Bromacker Quarry in Germany, and the second is Oromycter from the lower Permian of Richards Spur, Oklahoma. The former is known from several articulated skeletons, but the latter is known only from a handful of skeletal elements, including elements of the snout and lower jaw, some phalanges, and a few vertebrae. Here the fragmentary tooth bearing elements and dorsal vertebrae of another small caseid from Richards Spur are described, with a discussion of its significance in the context of caseid evolution, and the continuously expanding faunal list and taxic diversity at this locality

Dynamical Linked Cluster Expansions: A Novel Expansion Scheme for Point-Link-Point-Interactions

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. This amounts to a generalization from 2-point to point-link-point interactions. We develop an associated graph theory with a generalized notion of connectivity and describe an algorithmic generation of the new multiple-line graphs. We indicate physical applications to spin glasses, partially annealed neural networks and SU(N) gauge Higgs systems. In particular the new expansion technique provides the possibility of avoiding the replica-trick in spin glasses. We consider variational estimates for the SU(2) Higgs model of the electroweak phase transition. The results for the transition line, obtained by dynamical linked cluster expansions, agree quite well with corresponding high precision Monte Carlo results.Comment: 41 pages, latex2e, 10 postscript figure

A Juvenile Specimen of the Trematopid Acheloma From Richards Spur, Oklahoma and Challenges of Trematopid Ontogeny

Trematopids are a clade of terrestrial dissorophoid temnospondyls documented primarily from terrestrial Permo-Carboniferous environments in North America and Europe. Here we describe the complete skull and articulated mandibles of a diminutive trematopid specimen (OMNH 79318) from the Early Permian karst deposits near Richards Spur, Oklahoma. Based on aspects of the neurocranium (e.g., unossified sphenethmoid, prootics, epipterygoids), the specimen represents one of the best examples of a markedly immature trematopid, an important data point for understanding the early ontogeny of trematopids. Specifically, it provides evidence that variation in otic notch structure can be ontogenetically influenced, not only among eucacopine dissorophids but also among trematopids. We provisionally refer the specimen to cf. Acheloma based on the presence of a denticulate vomerine ridge and other qualitative features. However, we emphasize that the taxonomic referral is complicated by several factors that more broadly confound trematopid taxonomy. This includes a low sample size (n = 1) of many taxa and marked size, and presumed ontogenetic, disparity between the known size range of different taxa. Complementary reexamination of both Acheloma cumminsi and Acheloma dunni as part of this study also reveals that the former possesses lateral exposures of palatal bones, the presence/absence of which was the only formal character that previously differentiated the two species, although other qualitative features (e.g., size of the internarial fontanelle) may differentiate these two species. With respect to OMNH 79318, the taxonomic referral is tentative because the specimen also shares many qualitative attributes with Phonerpeton pricei, a trematopid represented only by small-bodied, probably immature individuals. However, many of these shared features are likely to be influenced by ontogeny or size. The subsequent challenges that we encountered in our taxonomic referral suggest that ontogeny may be confounding taxonomy in both diagnoses and phylogenetic analyses of trematopids and emphasize the need for careful study of how this affects our understanding of trematopid intrarelationships

A New Captorhinid From the Permian Cave System Near Richards Spur, Oklahoma, and the Taxic Diversity of Captorhinus at This Locality

The early Permian cave system in the Dolese Brothers Limestone Quarry near Richards Spur, Oklahoma represents a unique depositional environment that has been interpreted as preserving an upland biota. The quarry and the region around it represent Paleozoic cave systems that underwent periods of flooding not unlike present-day conditions that are commonly associated with monsoonal episodes. The Richards Spur locality is particularly rich in captorhinid eureptiles which represent one of the earliest reptilian clades to have evolved a specialized dentition. Although the multiple-tooth rowed Captorhinus aguti is the most abundant captorhinid at Richards Spur, at least one other species has been described (Captorhinus magnus) and assigned to the same genus, but five other captorhinid taxa have also been found. We describe a new member of the genus Captorhinus (Captorhinus kierani) and explore details of the dental anatomy against the two other members of the genus at Richards Spur, C. aguti and C. magnus, as well as with a member of the genus not presently known from Richards Spur (Captorhinus laticeps). Findings suggest that the nature of the ogival dentition described previously as a synapomorphy uniting C. aguti with C. magnus is not supported and we propose a more informative method for differentiating among dental characters within the clade. The discovery of a new species of Captorhinus provides additional evidence for captorhinid taxic diversity at Richards Spur and is supportive of niche partitioning, which is likely associated with reducing intra-specific competition within the clade. In addition, we argue that the captorhinid fossils at Richards Spur likely includes one additional, currently undescribed multiple-tooth rowed form, that renders the current practice of assigning disarticulated cranial remains, specifically dental fragments, to the species C. aguti problematic. Finally, we offer a method for a comprehensive examination of the dental characteristics, which can then be applied to explore taxic diversity at Richards Spur and examine one of the earliest examples of niche specialization. As a consequence of this research, additional insight into exploring biological interactions between Paleozoic taxa can be examined, with an opportunity to shed light on what might have driven these evolutionary processes

Critical Phenomena with Linked Cluster Expansions in a Finite Volume

Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish 1st from 2nd order transitions within a finite size scaling analysis. The criterion applies also to other methods for investigating the phase structure such as Monte Carlo simulations. Our computational tools are illustrated at the example of scalar O(N) models with four and six-point couplings for $N=1$ and $N=4$ in three dimensions. It is shown how to localize the tricritical line in these models. We indicate some further applications of our methods to the electroweak transition as well as to models for superconductivity.Comment: 36 pages, latex2e, 7 eps figures included, uuencoded, gzipped and tarred tex file hdth9607.te