Topic
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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TL;DR: In this article, the authors studied the algebra of FDA transformations and showed that the field theory based on the FDA is invariant under these new transformations, which gives geometrical meaning to the antisymmetric tensors.
Abstract: The gauging of free differential algebras (FDA's) produces gauge field theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer equations of ordinary Lie algebras by incorporating p-form potentials (p>1). We study here the algebra of FDA transformations. To every p-form in the FDA, we associate an extended Lie derivative l generating a corresponding ‘gauge’ transformation. The field theory based on the FDA is invariant under these new transformations. This gives geometrical meaning to the antisymmetric tensors. The algebra of Lie derivatives is shown to close and provides the dual formulation of FDA's.
26 citations
TL;DR: In this article, the theory of Schunck classes and projectors for soluble Leibniz algebras, parallel to that for Lie algesbras is presented.
Abstract: I set out the theory of Schunck classes and projectors for soluble Leibniz algebras, parallel to that for Lie algebras. Primitive Leibniz algebras come in pairs, one (Lie) symmetric, the other antisymmetric. A Schunck formation containing one member of a pair also contains the other. If ℌ is a Schunck formation and H is an ℌ-projector of the Leibniz algebra L, then H is intravariant in L. An example is given to show that the assumption that the Schunck class ℌ is a formation cannot be omitted.
26 citations
TL;DR: By applying this algorithm for solving the optimum nonuniform symmetric/antisymmetric linear phase finite-impulse-response (FIR) filter bank design problems, the time required to obtain a globally optimal solution is much reduced.
Abstract: An efficient algorithm for solving semi-infinite programming problems is proposed in this paper. The index set is constructed by adding only one of the most violated points in a refined set of grid points. By applying this algorithm for solving the optimum nonuniform symmetric/antisymmetric linear phase finite-impulse-response (FIR) filter bank design problems, the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorithm
26 citations
TL;DR: In this paper, the authors study the limit of the Rossby number e of the primitive equations of the atmosphere and the ocean, and study the averaging of a penalization problem displaying oscillations generated by an antisymmetric operator.
26 citations
TL;DR: This paper provides a comprehensive assessment of the current status of the nucleon form factors of the quark tensor using lattice QCD results in the meson sector and, in combination with pole dominance, extends this method to the nucleons case.
Abstract: If physics beyond the standard model enters well above the electroweak scale, its low-energy effects are described by standard model effective field theory. Already, at dimension 6, many operators involve the antisymmetric quark tensor q[over ¯]σ^{μν}q, whose matrix elements are difficult to constrain from experiment, Ward identities, or low-energy theorems, in contrast to the corresponding vector and axial-vector or even scalar and pseudoscalar currents. However, with normalizations determined from lattice QCD, analyticity and unitarity often allow one to predict the momentum dependence in a large kinematic range. Starting from recent results in the meson sector, we extend this method to the nucleon case and, in combination with pole dominance, provide a comprehensive assessment of the current status of the nucleon form factors of the quark tensor.
26 citations