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317 results on '"Natural field"'

2. Gauge-natural field theories and Noether Theorems: canonical covariant conserved currents

Author

Palese, Marcella and Winterroth, Ekkehart

Subjects
Mathematical Physics, 58A20, 58A32, 58E30, 58E40, 58J10, 58J70
Abstract

Recently we found that canonical gauge-natural superpotentials are obtained as global sections of the {\em reduced} $(n-2)$-degree and $(2s-1)$-order quotient sheaf on the fibered manifold $\bY_{\zet} \times_{\bX} \mathfrak{K}$, where $\mathfrak{K}$ is an appropriate subbundle of the vector bundle of (prolongations of) infinitesimal right-invariant automorphisms $\bar{\Xi}$. In this paper, we provide an alternative proof of the fact that the naturality property $\cL_{j_{s}\bar{\Xi}_{H}}\omega (\lambda, \mathfrak{K})=0$ holds true for the {\em new} Lagrangian $\omega (\lambda, \mathfrak{K})$ obtained contracting the Euler--Lagrange form of the original Lagrangian with $\bar{\Xi}_{V}\in \mathfrak{K}$. We use as fundamental tools an invariant decomposition formula of vertical morphisms due to Kol\'a\v{r} and the theory of iterated Lie derivatives of sections of fibered bundles. As a consequence, we recover the existence of a canonical generalized energy--momentum conserved tensor density associated with $\omega (\lambda, \mathfrak{K})$., Comment: 16 pages, abstract rewritten, body slightly revised, Proc. Winter School "Geometry and Physics" (Srni,CZ 2005)

Published
2005

3. Generalized Bianchi identities in gauge-natural field theories and the curvature of variational principles

Author

Francaviglia, M., Palese, M., and Winterroth, E.

Subjects
Mathematical Physics, Mathematics - Differential Geometry, 58A20, 58A32, 58E30
Abstract

By resorting to Noether's Second Theorem, we relate the generalized Bianchi identities for Lagrangian field theories on gauge-natural bundles with the kernel of the associated gauge-natural Jacobi morphism. A suitable definition of the curvature of gauge-natural variational principles can be consequently formulated in terms of the Hamiltonian connection canonically associated with a generalized Lagrangian obtained by contracting field equations., Comment: 12 pages, minor changes, references list updated; presented at XXXVI Symposium on Math. Phys., Torun 09/06-12/06/04; v4 to appear in Rep. Math. Phys

Published
2004
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24. Toward More Natural Field Testing of Classroom Materials.

Author

American Institutes for Research in the Behavioral Sciences, Palo Alto, CA., Lipe, Dewey, and Haveman, Jacqueline E.

Abstract

Issues associated with the evaluation of 61 educational curriculum units, which was conducted by the American Institutes for Research (AIR) are described. The units were adapted to the AIR Career Education Curriculum framework by creating 133 instructional units within which students could develop career skills in an orderly sequence. The evaluation process involved initial revision, field testing, and final revision of the units. During the initial revision, the needs of teachers, school administrators, and publishers were seen to include reduction in the length of units, inclusion of alternative learning activities, reduction in cost, replacement of copyrighted passages, and improvement in the appearance of materials. Obtaining information without arousing resentment or reluctance was described as the most difficult aspect of a naturalistic field test. As a result, teacher orientation workshops were conducted to introduce the curriculum units. School district responses were described as passive resistant, personally committed, aggressive resistant or group committed. Methods for obtaining unambiguous answers to test questions without disrupting the natural setting are described, and sample module and activity evaluation instruments are appended. Results included 454 teacher field test packets and 11,700 student evaluation forms. Computer-assisted handscoring of results is explained, as well as the development of total data sets for each module. (Author/JAC)

Published
1977

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