A Poincar\'e covariant cascade method for high-energy nuclear collisions

TL;DR

This paper introduces a Poincaré covariant cascade algorithm for simulating high-energy nuclear collisions, ensuring frame independence and reliability in complex dynamical scenarios.

Contribution

The paper develops a novel covariant cascade algorithm based on constrained Hamiltonian dynamics, extending traditional methods to an 8N-dimensional phase space for improved accuracy.

Findings

The covariant algorithm is validated through box calculations.

It demonstrates frame independence in expanding systems.

Efficient Lorentz-covariant equations of motion are derived.

Abstract

We present a Poincar\'e covariant cascade algorithm based on the constrained Hamiltonian dynamics in an $8N$-dimensional phase space to simulate the Boltzmann-type two-body collision term. We compare this covariant cascade algorithm with traditional $6N$-dimensional phase-space cascade algorithms. To validate the covariant cascade algorithm, we perform box calculations. We examine the frame dependence of the algorithm in a one-dimensionally expanding system as well as the compression stages of colliding two nuclei. We confirm that our covariant cascade method is reliable to simulate high-energy nuclear collisions. Furthermore, we present Lorentz-covariant equations of motion for the $N$-body system interacting via potentials, which can be efficiently solved numerically.