A simple way to generate high order vacuum graphs

We describe an efficient practical procedure for enumerating and regrouping vacuum Feynman graphs of a given order in perturbation theory. The method is based on a combination of Schwinger-Dyson equations and the two-particle-irreducible ("skeleton") expansion. The regrouping leads to skeletons containing only free propagators, together with "ring diagrams" containing all the self-energy insertions. As a consequence, relatively few diagrams need to be drawn and integrations carried out at any single stage of the computation and, in low dimensions, overlapping ultraviolet/infrared subdivergences can be cleanly isolated. As an illustration we enumerate the graphs contributing to the 4-loop free energy in QCD, explicitly in a continuum and more compactly in a lattice regularization.Comment: 19 pages. Reference added. To appear in Phys.Rev.

The middle ear of the pink fairy armadillo Chlamyphorus truncatus (Xenarthra, Cingulata, Chlamyphoridae): comparison with armadillo relatives using computed tomography.

The pink fairy armadillo Chlamyphorus truncatus is the smallest extant armadillo and one of the least-known fossorial mammals. The aim of this study was to establish if its middle ear is specially adapted to the subterranean environment, through comparison with more epigeic relatives of the groups Euphractinae (Chaetophractus villosus, Chaetophractus vellerosus, Zaedyus pichiy) and Dasypodinae (Dasypus hybridus). We examined the middle ears using micro-computed tomography and subsequent three-dimensional reconstructions. D. hybridus has a relatively small middle ear cavity, an incomplete bulla and 'ancestral' ossicular morphology. The other species, including Chlamyphorus, have fully ossified bullae and middle ear ossicles, with a morphology between 'transitional' and 'freely mobile', but in all armadillos the malleus retains a long anterior process. Unusual features of armadillo ears include the lack of a pedicellate lenticular apophysis and the presence, in some species, of an element of Paaw within the stapedius muscle. In common with many subterranean mammals, Chlamyphorus has a relatively flattened malleo-incudal articulation and appears to lack a functional tensor tympani muscle. Its middle ear cavity is not unusually enlarged, and its middle ear ossicles seem less robust than those of the other armadillos studied. In comparison with the euphractines, there is no reason to believe that the middle ear of this species is specially adapted to the subterranean environment; some aspects may even be indicative of degeneration. The screaming hairy armadillo, Chaetophractus vellerosus, has the most voluminous middle ear in both relative and absolute terms. Its hypertrophied middle ear cavity likely represents an adaptation to low-frequency hearing in arid rather than subterranean conditions.Argentinian research grants: Secretaría General de Ciencia y Tecnología, UNS (Project PGI 24/B243); Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) through a PhD fellowship to APB; Subsecretaría de Relaciones Internacionales, UNS, through a grant to APB

Manifest covariance and the Hamiltonian approach to mass gap in (2+1)-dimensional Yang-Mills theory

In earlier work we have given a Hamiltonian analysis of Yang-Mills theory in (2+1) dimensions showing how a mass gap could arise. In this paper, generalizing and covariantizing from the mass term in the Hamiltonian analysis, we obtain two manifestly covariant and gauge-invariant mass terms which can be used in a resummation of standard perturbation theory to study properties of the mass gap.Comment: Sections 1, 4 modified, part of section 2 moved to appendix, 19 pages, LaTe