Annales Henri Poincaré

, Volume 19, Issue 5, pp 1385–1417 | Cite as

Super-Quantum Mechanics in the Integral Form Formalism

  • L. Castellani
  • R. Catenacci
  • P. A. Grassi


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.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • L. Castellani
    • 1
    • 2
    • 3
  • R. Catenacci
    • 1
    • 3
    • 4
  • P. A. Grassi
    • 1
    • 2
    • 3
    • 5
  1. 1.Dipartimento di Scienze e Innovazione TecnologicaUniversità del Piemonte OrientaleAlessandriaItaly
  2. 2.INFN, Sezione di TorinoTurinItaly
  3. 3.Arnold-Regge CenterTurinItaly
  4. 4.Gruppo Nazionale di Fisica MatematicaINdAMRomeItaly
  5. 5.Center for Gravitational Physics Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan

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