# Quantum objects in a sheaf framework

## TL;DR

This paper proposes a sheaf-theoretic framework for quantum states, aiming to deepen understanding of quantum phenomena through the use of sheaves with multiscale filtrations and internal symmetries.

## Contribution

It introduces a novel sheaf-based approach to quantum states that incorporates multiscale filtrations and hidden symmetries for better conceptual understanding.

## Key findings

- Provides a new sheaf-theoretic model for quantum states
- Enables reinterpretation of quantum phenomena
- Suggests potential for exact descriptions of quantum effects

## Abstract

We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the proposed construction are the families of sections of sheaves with values in the proper category of the functional realizations of infinite-dimensional Hilbert spaces with special (multiscale) filtrations decomposed into the (entangled) orbits generated by actions/representations of internal hidden symmetries. In such a way, we open a possibility for the exact description and reinterpretation of a lot of quantum phenomena.