# Lorentz-invariant second-order tensors and an irreducible set of matrices

## TL;DR

This paper proves that the Minkowski metric tensor is uniquely Lorentz-invariant among second-order tensors, using the irreducibility of a specific set of matrices composed of rotations and boosts.

## Contribution

It establishes the uniqueness of the Minkowski metric tensor as the only Lorentz-invariant second-order tensor, demonstrating the irreducibility of a key matrix set.

## Key findings

- Minkowski metric tensor is unique up to scalar multiplication.
- A specific set of matrices is irreducible under Lorentz transformations.
- The proof relies on the irreducibility of rotation and boost matrices.

## Abstract

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.