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Tractors and Twistors bundles both provide natural conformally covariantcalculi on $4D$-Riemannian manifolds. They have different origins but areclosely related, and usually constructed bottom-up from prolongation ofdefining differential equations. We propose alternative top-down gaugetheoretic constructions starting from the conformal Cartan bundle and itsvectorial and spinorial associated bundles. Our key ingredient is the dressingfield method of gauge symmetry reduction, which allows to exhibit tractors andtwistors and their associated connections as gauge field of a non-standard kindas far as Weyl rescaling symmetry is concerned. By which we mean that theyimplement the gauge principle but are of a different geometric nature than thewell known differential geometric objects usually underlying gauge theories. Weprovide the corresponding BRST treatment. The present paper deals with the caseof tractors while a companion paper deals with twistors.

Tractors and Twistors from conformal Cartan geometry: a gauge theoretic approach I. Tractors