2017/06/30 by L. Castellani, R. Catenacci, P. A. Grassi
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Context (archaeology) #Dual polyhedron #Formalism (music) #Hilbert space #Noncommutative and Quantum Gravity Theories #Path integral formulation #Space (punctuation) #Superspace #Surface integral #hep-th
paper · pdf · doi:10.1007/s00023-018-0653-y
41 pages, no figures. Use birkjour.cls. Minor misprints, moved appendix A and B in the main text. Version to be published in Annales H. Poincaré
openalex created_date 2017/06/23 · arxiv created 2017/11/06 · openalex publication_date 2018/02/23 · arxiv updated 2018/05/09 · openalex updated_date 2026/08/05
We reformulate Super Quantum Mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of Picture Changing Operators (PCO). In this way we retrieve component and superspace actions, and prove their equivalence. The PCO are closed integral forms, and can be interpreted as super Poincaré duals of bosonic submanifolds embedded into a supermanifold.. We use them to construct Lagrangians that are top integral forms, and therefore can be integrated on the whole supermanifold. The D=1, ~N=1 and the D=1,~ N=2 cases are studied, in a flat and in a curved supermanifold. In this formalism we also consider coupling with gauge fields, Hilbert space of quantum states and observables.