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We provide a model independent construction of a net of C*-algebrassatisfying the Haag-Kastler axioms over any spacetime manifold. Such a net,called the net of causal loops, is constructed by selecting a suitable base Kencoding causal and symmetry properties of the spacetime. Considering K as apartially ordered set (poset) with respect to the inclusion order relation, wedefine groups of closed paths (loops) formed by the elements of K. These groupscome equipped with a causal disjointness relation and an action of the symmetrygroup of the spacetime. In this way the local algebras of the net are the groupC*-algebras of the groups of loops, quotiented by the causal disjointnessrelation. We also provide a geometric interpretation of a class ofrepresentations of this net in terms of causal and covariant connections of theposet K. In the case of the Minkowski spacetime, we prove the existence ofPoincar\'e covariant representations satisfying the spectrum condition. This isobtained by virtue of a remarkable feature of our construction: any Hermitianscalar quantum field defines causal and covariant connections of K. Similarresults hold for the chiral spacetime $S^1$ with conformal symmetry.

Causal posets, loops and the construction of nets of local algebras for QFT