# Quantization of dynamical symplectic reduction

## TL;DR

This paper addresses the challenge of quantizing constrained dynamical systems in quantum gravity, proposing an algebraic framework with new structures to ensure well-defined evolution.

## Contribution

It introduces an algebraic formulation of the quantization problem for constrained systems and identifies conditions for consistent evolution.

## Key findings

- New algebraic structures for quantization
- Conditions for well-defined quantum evolution
- Framework applicable to quantum gravity models

## Abstract

A long-standing problem in quantum gravity and cosmology is the quantization of systems in which time evolution is generated by a constraint that must vanish on solutions. Here, an algebraic formulation of this problem is presented, together with new structures and results, which show that specific conditions need to be satisfied in order for well-defined evolution to be possible.