Webmetric 2-tensor, sometimes called the notoph [1] or the Kalb-Ramond field [2]. These theories have some elegant properties, including dualities to other p-form theories [1–3]. In this work, we consider Lorentz-violating field theo-ries with an antisymmetric 2-tensor, including models coupled to gravity. In a generic Lagrange density, terms http://jakobschwichtenberg.com/vectors-forms-p-vectors-p-forms-and-tensors/

Tensors and Pseudo-Tensors - University of Texas at Austin

A tensor whose components in an orthonormal basis are given by the Levi-Civita symbol (a tensor of covariant rank n) is sometimes called a permutation tensor. Under the ordinary transformation rules for tensors the Levi-Civita symbol is unchanged under pure rotations, consistent with that it is (by definition) the same in all coordinate systems related by orthogonal transformations. However, the Levi-Civita symbol is a pseudotensor because unde… Websubstract as there are components in a tensor of rank r 2. The total number of independent components in a totally symmetric traceless tensor is then d+ r 1 r d+ r 3 r 2 3 Totally anti … crystal keepers read online free

Symmetry Free Full-Text Energy-Momentum Relocalization, …

WebAug 21, 2015 · Tensors. Tensors are the natural generalization of the ideas described above. Tensors are linear operators on vectors and one-forms. ... If the tensor has more than two arguments of the same kind, the tensor is said to be totally antisymmetric (symmetric) if it is antisymmetric ... WebThe fact that the components of the four-tensor are unchanged under rotations of a four-dimensional coordinate system, and that the components of the three-tensor are unchanged by rotations of the space axes are special cases of a general rule: any completely antisymmetric tensor of rank equal to the number of dimensions of the space in which it … WebSince a covariantly conserved antisymmetric rank-n tensor field is equivalent to a co-closed n-form, one can use the extension of the Poincaré lemma to the exterior co-derivative and express the original rank-n tensor field as the co-derivative of an (n + 1)-form in a suitably chosen (simply-connected) open set. dwight o\\u0027hara financial advisor