# Super Quantum Mechanics in the Integral Form Formalism

## TL;DR

This paper introduces a reformulation of Super Quantum Mechanics using integral forms, enabling interpolation between different actions and unifying component and superspace formulations through the use of Picture Changing Operators.

## Contribution

It presents a novel integral form framework for Super Quantum Mechanics, connecting various actions and including gauge coupling and quantum states analysis.

## Key findings

- Unified component and superspace actions
- Constructed top integral form Lagrangians
- Analyzed flat and curved supermanifolds

## 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 Poincar\'e 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.