# Hamiltonian Theory: Dynamics

**Authors:** Thomas Thiemann, Kristina Giesel  
**arXiv:** [2303.18172](https://arxiv.org/abs/2303.18172)  
**Date:** 2023-03-31  
**Summary page:** https://www.summarizepaper.com/en/paper/2303.18172v1/

## Key points

- Thiemann and Giesel's chapter provides an overview of the current status of dynamics in Loop Quantum Gravity (LQG).
- The focus is on giving a mathematical meaning to the quantum Einstein equations and constructing a representation of the algebra of observables that includes a physical Hamiltonian.
- The authors aim to provide a physical interpretation and Hilbert space structure to the solutions obtained from these equations.
- This chapter intentionally skips technical details and serves as a structural overview.
- LQG is still an active area of research with many open questions and challenges.
- The chapter is part of the upcoming "Handbook of Quantum Gravity," edited by Cosimo Bambi, Leonardo Modesto, and Ilya Shapiro which will be published by Springer in 2023.

## Summary

In their chapter titled "Hamiltonian Theory: Dynamics," Thomas Thiemann and Kristina Giesel provide an overview of the current status of the implementation of dynamics in Loop Quantum Gravity (LQG). Specifically, they focus on providing a mathematical meaning to the quantum Einstein equations, also known as Wheeler-DeWitt equations, and constructing a representation of the algebra of observables that includes a physical Hamiltonian. The authors aim to give a physical interpretation and Hilbert space structure to the solutions obtained from these equations. This chapter is intended as a structural overview which intentionally skips technical details. The authors note that LQG is still an active area of research with many open questions and challenges. However, they hope that this overview will serve as a useful guide for researchers interested in understanding the current state of dynamics in LQG. This chapter is part of the upcoming "Handbook of Quantum Gravity," edited by Cosimo Bambi, Leonardo Modesto, and Ilya Shapiro which will be published by Springer in 2023.