Document Zbl 1411.15019

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Lorentz-invariant second-order tensors and an irreducible set of matrices. (English) Zbl 1411.15019

J. Geom. Symmetry Phys. 50, 1-10 (2018).

Summary: We prove that, up to multiplication by a scalar, the Minkowski metric tensor is the only second-order tensor that is Lorentz-invariant. To prove this, we show that a specific set of three \(4\times 4\) matrices, made of two rotation matrices plus a Lorentz boost, is irreducible.

MSC:

15A72	Vector and tensor algebra, theory of invariants
51B20	Minkowski geometries in nonlinear incidence geometry
83A05	Special relativity
22E43	Structure and representation of the Lorentz group

Keywords:

irreducible set of matrices; linear algebra; Lorentz group; Minkowski metric

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