Quantum seminar | 24 September 2025

According to Noether theorem, energy is an integral of motion in theories which possess an invariance w.r.t. time shifts. However, in theories with time reparametrization symmetry this integral of motion becomes more difficult to define. We review some basic properties of systems with such symmetry and discuss a few specific cases in which this problem must be dealt with: namely, a relativistic particle and general relativity. By analogy with the case of relativistic particle, we propose a way to define energy in general relativistic case using the procedure of isometric embedding.

Main paper/arXiv, related to the seminar, and other references

A. A. Sheykin, Yet another way from field theory to gravity, arXiv:2402.02891 [gr-qc]