Barnich--Troessaert bracket as a Dirac bracket on the covariant phase space

The Barnich--Troessaert bracket is a proposal for a modified Poisson bracket on the covariant phase space for general relativity. The new bracket allows us to compute charges, which are otherwise not integrable. Yet there is a catch. There is a clear prescription for how to evaluate the new bracket for any such charge, but little is known how to extend the bracket to the entire phase space. This is a problem, because not every gravitational observable is also a charge. In this paper, we propose such an extension. The basic idea is to remove the radiative data from the covariant phase space. This requires second-class constraints. Given a few basic assumptions, we show that the resulting Dirac bracket on the constraint surface is nothing but the BT bracket. A heuristic argument is given to show that the resulting constraint surface can only contain gravitational edge modes.

Instanton worldlines in five-dimensional Ω-deformed gauge theory

We discuss the Bosonic sector of a class of supersymmetric non-Lorentzian five-dimensional gauge field theories with an SU(1, 3) conformal symmetry. These actions have a Lagrange multiplier which imposes a novel Ω-deformed anti-self-dual gauge field constraint. Using a generalised ’t Hooft ansatz we find the constraint equation linearizes allowing us to construct a wide class of explicit solutions. These include finite action configurations that describe worldlines of anti-instantons which can be created and annihilated. We also describe the dynamics on the constraint surface.

Erratum to: Gravitons in a Casimir box

The correct name of the second author is Martin Bonte. In the expression for the Pauli-Fierz Hamiltonian in equation (3.10), we missed two terms that vanish on the constraint surface.

An Ising Spin-Based Model to Explore Efficient Flexibility in Distributed Power Systems

This paper analyses customers’ demand flexibility in a local power trading scenario through an Ising spin-based model. We look at quantitative information on the two-way relationships between power exchanges and spin dynamics. To this end, a modified version of the Metropolis-Hastings algorithm was implemented, including a gradient descent through the constraint surface. This allowed us to analyse the system on a large scale (considering the cumulated benefit of all the actors involved) and also from the perspective of total aggregation. In a maximum flexibility scenario, the total aggregation profit increases with the number of aggregators. We also investigate numerically the effect of aggregator boundaries on the spin dynamics.