xCPS: an xAct package for covariant phase space, Noether charges, and entropy

Abstract

xCPS is an xAct tensor algebra package for symbolic computations within the covariant phase space formalism of field theories. From a generic Lagrangian, xCPS automates the derivation of equations of motion and symplectic currents. It systematically determines whether an infinitesimal transformation in the space of fields is a Noether symmetry and computes the associated Noether charge. Additionally, xCPS can in many cases determine whether a tensorial expression is a divergence and, if so, find its divergence potential. By implementing vertical exterior calculus through a graded, supercommutative wedge product and vertical operators, the package enables efficient computations in gauge theories and higher-derivative models of gravity, including the derivation of thermodynamic quantities like Wald's entropy. xCPS is open-source under the GPL license and available at https://github.com/juanmargalef.