Super Quantum Mechanics in the Integral Form Formalism

Abstract

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.

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

References in corpus (7)

• Superbranes and Superembeddings
• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• Supergravity Actions with Integral Forms
• The Geometry of Supermanifolds and New Supersymmetric Actions
• Hodge Dualities on Supermanifolds
• Cech and de Rham Cohomology of Integral Forms
• The Minkowski and conformal superspaces

Cited by in corpus (5)

• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• On the Geometry of Forms on Supermanifolds
• Supergravities and Branes from Hilbert-Poincaré Series
• Wess-Zumino and Super Yang-Mills Theories in D=4 Integral Superspace
• Chern-Simons Supergravity on Supergroup Manifolds