# Schwinger's Picture of Quantum Mechanics I: Groupoids

## TL;DR

This paper introduces a novel framework for quantum mechanics using groupoids, providing a categorical foundation that connects Schwinger's measurement algebra with standard quantum formalisms.

## Contribution

It develops a categorical, groupoid-based mathematical background for quantum mechanics, linking Schwinger's algebra to existing quantum theories.

## Key findings

- Introduces the use of 2-groupoids in quantum kinematics
- Establishes connections with Dirac-Schrödinger and Heisenberg pictures
- Provides foundational results on groupoid representations in quantum theory

## Abstract

A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger's algebra of selective measurements and helps to understand its scope and eventual applications. In this first paper, the kinematical background is described using elementary notions from category theory, in particular the notion of 2-groupoids as well as their representations. Some basic results are presented, and the relation with the standard Dirac-Schr\"odinger and Born-Jordan-Heisenberg pictures are succinctly discussed.