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If a tensor A is defined on a vector fields set X(M) over a module M, we call A a tensor field on M. [1] Many mathematical structures called "tensors" are also tensor fields. For example, the Riemann curvature tensor is a tensor field as it associates a tensor to each point of a Riemannian manifold, which is a topological space.
The stresses inside a solid body or fluid [28] are described by a tensor field. The stress tensor and strain tensor are both second-order tensor fields, and are related in a general linear elastic material by a fourth-order elasticity tensor field. In detail, the tensor quantifying stress in a 3-dimensional solid object has components that can ...
A field can be classified as a scalar field, a vector field, a spinor field or a tensor field according to whether the represented physical quantity is a scalar, a vector, a spinor, or a tensor, respectively. A field has a consistent tensorial character wherever it is defined: i.e. a field cannot be a scalar field somewhere and a vector field ...
In theoretical physics in general and string theory in particular, the Kalb–Ramond field (named after Michael Kalb and Pierre Ramond), [1] also known as the Kalb–Ramond B-field [2] or Kalb–Ramond NS–NS B-field, [3] is a quantum field that transforms as a two-form, i.e., an antisymmetric tensor field with two indices.
The field tensor was first used after the four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows related physical laws to be written concisely, and allows for the quantization of the electromagnetic field by the Lagrangian formulation described below .
The algebraic classification of bivectors given above has an important application in relativistic physics: the electromagnetic field is represented by a skew-symmetric second rank tensor field (the electromagnetic field tensor) so we immediately obtain an algebraic classification of electromagnetic fields.
[a] [1] [2] [3] It is also the modern name for what used to be called the absolute differential calculus (the foundation of tensor calculus), tensor calculus or tensor analysis developed by Gregorio Ricci-Curbastro in 1887–1896, and subsequently popularized in a paper written with his pupil Tullio Levi-Civita in 1900. [4]
In mathematics, a tensor is a certain kind of geometrical entity and array concept. It generalizes the concepts of scalar , vector and linear operator , in a way that is independent of any chosen frame of reference .
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