1,720,961 research outputs found
Gauge theories on manifolds with boundary
No full textThe boundary-value problem for Laplace-type operators acting on smooth
sections of a vector bundle over a compact Riemannian manifold with generalized local
boundary conditions including both normal and tangential derivatives is studied. The
condition of strong ellipticity of this boundary-value problem is formulated. The resolvent
kernel and the heat kernel in the leading approximation are explicitly constructed.
As a result, the previous work in the literature on heat-kernel asymptotics is shown to
be a particular case of a more general structure. For a bosonic gauge theory on a compact
Riemannian manifold with smooth boundary, the problem of obtaining a gauge-field
operator of Laplace type is studied, jointly with local and gauge-invariant boundary conditions,
which should lead to a strongly elliptic boundary-value problem. The scheme is
extended to fermionic gauge theories by means of local and gauge-invariant projectors.
After deriving a general condition for the validity of strong ellipticity for gauge theories,
it is proved that for Euclidean Yang–Mills theory and Rarita–Schwinger fields all the
above conditions can be satisfied. For Euclidean quantum gravity, however, this property
no longer holds, i.e. the corresponding boundary-value problem is not strongly elliptic.
Some non-standard local formulae for the leading asymptotics of the heat-kernel diagonal
are also obtained. It is shown that, due to the lack of strong ellipticity, the heat-kernel
diagonal is non-integrable near the boundary
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
New invariants in the 1-loop divergences on manifolds with boundary
No full textThe quantization of gauge fields and gravitation on manifolds with boundary makes
it necessary to study boundary conditions which involve both normal and tangential derivatives of
the quantized field. The resulting 1-loop divergences can be studied by means of the asymptotic
expansion of the heat kernel, and a particular case of their general structure is analysed here
in detail. The interior and boundary contributions to heat-kernel coefficients are written as
linear combinations of all geometric invariants of the problem. The behaviour of the differential
operator and of the heat kernel under conformal rescalings of the background metric leads to
recurrence relations which, jointly with the boundary conditions, may determine these linear
combinations. Remarkably, they are expressed in terms of universal functions, independent of
the dimension of the background and invariant under conformal rescalings, and new geometric
invariants contribute to heat-kernel asymptotics. Such a technique is applied to the evaluation
of the A_{1} coefficient when the matrices occurring in the boundary operator commute with each
other. Under these assumptions, the form of the A_{3/2} and A_{2} coefficients is obtained for the
first time, and new equations among universal functions are derived. A generalized formula,
relating asymptotic heat kernels with different boundary conditions, is also obtained
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
On ellipticity and gauge invariance in Euclidean quantum gravity
No full textInvariance principles determine many key properties in quantum field theory, including, in particular, the appropriate form of the boundary conditions. A crucial consistency check is the proof that the resulting boundary-value problem is strongly elliptic. In Euclidean quantum gravity, the appropriate principle seems to be the invariance of boundary conditions under infinitesimal diffeomorphisms on metric perturbations, and hence their BRST invariance. However, if the operator on metric perturbations is then chosen to be of Laplace type, the boundary-value problem for the quantized gravitational field fails to be strongly elliptic. A detailed proof is presented, and the corresponding open problems are discussed
Heat-kernel asymptotics of the Gilkey--Smith boundary-value problem
No full textThe formulation of gauge theories on compact Riemannian manifolds with boundary leads to partial differential operators with Gilkey–Smith boundary conditions, whose peculiar property is the occurrence of both normal and tangential derivatives on the boundary. Unlike the standard Dirichlet or Neumann boundary conditions, this boundary-value problem is not automatically elliptic but becomes elliptic under certain conditions on the boundary operator. We study the Gilkey–Smith boundary-value problem for Laplace-type operators and find a simple criterion of ellipticity. The first non-trivial coefficient of the asymptotic expansion of the trace of the heat kernel is computed and the local leading asymptotics of the heat-kernel diagonal is also obtained. It is shown that, in the non-elliptic case, the heat-kernel diagonal is non-integrable near the boundary, which reflects the fact that the heat kernel is not of trace class. We apply this analysis to general linear bosonic gauge theories and find an explicit condition of ellipticity
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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