# Constrained projective quantum states for the degenerate Plebanski gravity

## TL;DR

This paper constructs projective quantum states for degenerate Plebanski gravity that incorporate the theory's constraints, advancing the development of quantum states aligned with the dynamics of such theories.

## Contribution

It introduces a method to build constrained projective quantum states for degenerate Plebanski gravity, addressing the gap of constraint incorporation in previous kinematic constructions.

## Key findings

- Successfully constructed constrained quantum states for the toy-theory
- Demonstrated compatibility with the theory's constraints
- Provides a foundation for more realistic quantum gravity models

## Abstract

Nowadays projective quantum states can be constructed for a number of field theories including Loop Quantum Gravity. However, these states are kinematic in this sense that their construction does not take into account the dynamics of the theories. In particular, the construction neglects constraints on phase spaces. Here we present projective quantum states for a "toy-theory" called degenerate Plebanski gravity which satisfy a constraint of this theory.