**2. Bundle Structure**

The introduction of a metric *g* and an orthogonality relation via a minkowskian metric *η* are two fundamental ingredients for building up a fiber bundle where we want the orthogonal group to act freely and transitively on the fibers. This will allow us to have a principal connection and to see the perfect analogy with an ordinary gauge theory ([1] chapter III).

Such a construction underlies the concept of *principal bundle*, and tetrads will be an isomorphism from the tangent bundle<sup>1</sup> *TM* to an associated bundle <sup>V</sup>.
