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Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.


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Journal ArticleDOI
TL;DR: The Atiyah-Singer index theorem for even-dimensional orientable manifolds without boundary with totally antisymmetric torsion with vanishing curl was proved in this article.
Abstract: The author presents two proofs of the Atiyah-Singer index theorem (1969) for the Dirac operator for even-dimensional orientable manifolds without boundary with totally antisymmetric torsion with vanishing curl (H torsion) which, for example, may be provided by the field strength of the antisymmetric tensor occurring in the supergravity multiplet of superstring-inspired ten-dimensional theories, or by the structure constants of the group manifold in Kaluza-Klein theories. One of the methods, which is considered as formal, utilises a modified version of the conventional heat kernel regularisation. The other which is shown to be connected to the first one through a Legendre transformation uses the supersymmetric path integral approach. Of course, as far as the index is concerned, the H parts form a globally defined exact form and hence the author's result is consistent with the invariance of the index under the inclusion of torsion. The obvious advantage of the author's approach is the simplicity of the calculations in contrast to conventional regularisation methods which are practically impossible to handle beyond four dimensions, despite the trivial effects of the torsion on the (physical) results.

54 citations

Journal ArticleDOI
TL;DR: In this paper, a type of resonant add/drop filter based on the excitation of degenerate symmetric and antisymmetric modes is analyzed and the resulting analytic expressions lead to an equivalent circuit and the transfer characteristics of the filter are related to standard L-C circuits.
Abstract: Time-dependent mode-coupling theory is used to analyze a type of resonant add/drop filter based on the excitation of degenerate symmetric and antisymmetric modes. Flat-top transfer functions are achieved with higher order filters that utilize multiple resonator pairs, designed to satisfy the degeneracy conditions. The resulting analytic expressions lead to an equivalent circuit and the transfer characteristics of the filter are related to standard L-C circuit designs.

54 citations

Journal ArticleDOI
TL;DR: In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is shown in this paper, where the authors explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.
Abstract: The coefficient of the dimensionally regularized two-loop R 3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. As a result, we explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.

54 citations

Journal ArticleDOI
TL;DR: In this article, the authors extended the Rayleigh theory to study the interface instability of axisymmetric gas-liquid flows and derived dispersion equations of cylindrical liquid sheets.
Abstract: This paper extends the Rayleigh theory to study the interface instability of axisymmetric gas-liquid flows. The dispersion equations of cylindrical liquid sheets were derived and numerical solutions were obtained. Two families of instability curves were found; one for symmetric disturbances and the other for antisymmetric disturbances. Two limiting cases can be recovered from derived dispersion equations. The equation recovers the Rayleigh instability of round jets for symmetric disturbances and recovers the hollow jet or submerged jet instability for antisymmetric disturbances. Effects due to ambient fluid density and ambient fluid velocity on liquid-sheet instabilities were examined.

54 citations

Journal ArticleDOI
TL;DR: In this paper, a detailed, three-dimensional stress and displacement analysis of transversely loaded, laminated complete hollow cylinders and open cylindrical panels having a symmetric or an antisymmetric cross-ply lay-up is presented.

54 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023145
2022286
2021109
2020112
2019118
2018122