125k views
5 votes
Is there some kind of completeness relation linking a set of four orthogonal (orthonormal) vectors in Minkowski space to the metric Diag(1, -1, -1, -1)? I tried to look this up online but found nothing.

1 Answer

4 votes

Final answer:

A set of four orthogonal (or orthonormal) vectors in Minkowski space can be linked to the metric Diag(1, -1, -1, -1) through a completeness relation, which expresses the metric tensor as a sum of outer products of the orthogonal vectors.

Step-by-step explanation:

In Minkowski space, a set of four orthogonal (or orthonormal) vectors can be linked to the metric Diag(1, -1, -1, -1) through a completeness relation. The completeness relation expresses the metric tensor as a sum of outer products of the orthogonal vectors. In this case, the completeness relation is:

g = v1⊗v1 - v2⊗v2 - v3⊗v3 - v4⊗v4

Here, ⊗ denotes the outer product and g represents the metric tensor. The relation ensures that the metric tensor is properly represented by the given set of orthogonal vectors.

User Lander Van Breda
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories