PSALTer: Particle Spectrum for Any Tensor Lagrangian

TL;DR

PSALTer is a software tool that automates the computation of particle spectra, masses, and unitarity conditions for tensor field theories, facilitating analysis of complex higher-rank theories efficiently.

Contribution

The paper introduces PSALTer, a novel software that automates spectral analysis for tensor Lagrangians, including higher-spin and gravity theories, with efficient computation and parallelization.

Findings

Computes particle spectra and unitarity conditions automatically.

Handles higher-rank tensor fields and complex gravity theories.

Runs efficiently on personal and high-performance computers.

Abstract

We present the PSALTer software for efficiently computing the mass and energy of the particle spectrum for any (e.g. higher-rank) tensor field theory in the Wolfram Language. The user must provide a Lagrangian density which is expanded quadratically in the fields around a Minkowski vacuum, is linear in the coupling coefficients, and otherwise built from the partial derivative and Minkowski metric. PSALTer automatically computes the spin-projection operators, saturated propagator, bare masses, residues of massive and massless poles and overall unitarity conditions in terms of the coupling coefficients. The constraints on the source currents and total number of gauge symmetries are produced as a by-product. We provide examples from scalar, vector, tensor and gauge theories of gravity. Each example, including spectra of higher-spin modified gravity theories, may be obtained on a personal computer in a matter of minutes. The software is also parallelised for use on high-performance computing resources. The initial release allows for parity-preserving operators constructed from fields of up to rank three: this functionality will be extended in future versions. PSALTer is a contribution to the xAct project.