In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space or manifold) or of the physical space.

Compute the transformation rules for each of the following, and hence decide whether or not they are tensors. Sub-and superscripted quantities (other than coordinates) are understood to be tensors.

It immediately follows that a scalar field is a zeroth-order tensor field, and a vector field is a first-order tensor field. Most tensor fields encountered in physics are smoothly varying and differentiable.

Vectors are simple and well-known examples of tensors, but there is much more to tensor theory than vectors. The second chapter discusses tensor fields and curvilinear coordinates. It is this chapter …

What is the difference between a tensor and tensor field? Usually, a tensor field of a manifold M M is an assignment of a tensor to each point of M M. Just like a vector field of M M gives you a vector at a …

* Tensors and physical theories: A commonplace attributed to Kretschmann states that any local physical theory can be represented in arbitrary coordinates using tensor calculus, but this may not be …

Jun 13, 2025 · Tensor fields are a fundamental concept in field theory, playing a crucial role in describing various physical phenomena in physics and engineering. In this article, we will explore the definition, …

A tensor bundle is built by attaching the associated tensor product vector space to each point of the manifold. Tensor fields are obtained as sections of the tensor bundle.

Note that if a Lie group G acts on a manifold X, then it automatically acts on the tangent bundle T X and thus on vector and, more generally, tensor elds on X. In particular, G acts on tensor elds on itself by …

In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the …