Special generalized densities and propagators: a geometric account

Abstract

Starting from a short review of spaces of generalized sections of vector bundles, we give a concise systematic description, in precise geometric terms, of Leray densities, principal value densities, propagators and elementary solutions of field equations in flat spacetime. We then sketch a partly original geometric presentation of free quantum fields and show how propagators arise from their graded commutators in the boson and fermion cases.

3+34 pages; various corrections and additions have been made in this second version

References in corpus (4)

• "Minimal geometric data" approach to Dirac algebra, spinor groups and field theories
• Frölicher-smooth geometries, quantum jet bundles and BRST symmetry
• Fiber bundle description of number scaling in gauge theory and geometry
• On the geometry of ghosts

Cited by in corpus (2)

• Gauge field theory without groups
• On semi-vector spaces and semi-algebras