Retrieving "Tensor" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Locality

   Linked via "tensors"

   Beyond physics, the term locality is used extensively in mathematics, particularly in topology and geometry. Here, locality refers to properties that hold true within an arbitrarily small neighborhood around a point, without requiring global constraints.
   For instance, a topological space $X$ is locally connected if every point $x \in X$ has a basis of arbitrarily small, connected neighborhoods. This contrasts sharply with global connectivity, which describes the entire space. In differential geometry, the concepts of tensors…

2. Lorentz Group

   Linked via "tensors"

   The representation theory of $SO^+(1, 3)$ is complex because it is a non-compact group. However, its double cover, $SL(2, \mathbb{C})$, is isomorphic to $SU(2) \times SU(2)$. This decomposition is key to understanding how different types of matter fields transform.
   Fields that transform under the two-valued representations of $SL(2, \mathbb{C})$ are classified based on how they transform under rotations ($\text{SU}(2)$) and boosts. Particles are often described by [tensors](/entr…