Super fiber bundles, connection forms, and parallel transport

The present work provides a mathematically rigorous account on super fiber bundle theory, connection forms and their parallel transport, that ties together various approaches. We begin with detailed introduction to bundles. then introduce the concept of so-called relative supermanifolds as well bundles connections defined in these categories. Studying objects turns out be utmost importance order to, among other things, model anticommuting classical fermionic fields mathematical physics. construct transport map corresponding such compare results those found by means literature. Finally, applications methods supergravity will discussed Cartan geometric formulation Poincar\'e description Killing vector spinors Riemannian manifolds arising from metric reductive geometries.