Formulation of fully covariant Quantum-Molecular Dynamics for an N-body system with scalar and vector potentials

TL;DR

This work addresses the need for a fully covariant description of relativistic N-body dynamics with both scalar and vector interactions. The authors derive covariant equations of motion using Dirac constraint dynamics, ensuring frame-independent evolution and a proper non-relativistic limit, and explore how different time constraints influence the formalism. They demonstrate the framework on two- and four-body scattering, clarifying connections to established transport models (RQMD, UrQMD, JAM) and highlighting the distinct dynamical roles of scalar versus vector fields. The resulting general N-body EoM provides a scalable foundation for studying strongly interacting matter in high-energy nuclear physics and related contexts, with potential applications to heavy-ion collisions and quark-gluon plasma dynamics.

Abstract

We present a fully covariant transport framework for Molecular Dynamics that enables a consistent description of the evolution of relativistic N-body systems. For the first time, we derive relativistic equations of motion incorporating both scalar and vector interactions within a manifestly covariant formulation. This approach addresses several fundamental issues in relativistic many-body dynamics: the implications of different choices of time-constraints, the emergence of the non-relativistic limit, the frame independence of the system's evolution, and the distinct dynamical roles of scalar and vector potentials. These aspects are investigated in detail for the scattering of two- and four-body systems, offering new insights into the consistency and physical interpretation of relativistic interactions in a covariant setting.

Figures (12)

• Figure 1: The sketch of the two particle system with different kinds of time constraints. The blue and red curves are trajectories of particle 1 and 2, respectively.
• Figure 2: The coordinates and momenta of particles 1 (solid lines) and 2 (dashed lines) as a function of computational time $\tau$ in relativistic evolutions. The red and blue lines represent an attractive ($c=1$) and a repulsive interaction ($c=-1$), respectively. The initial condition I is taken.
• Figure 3: The coordinates and momenta of particle 1 (solid lines) and 2 (dashed lines). The black and red line represent the non-relativistic and relativistic evolution with a mass $m=20~\rm GeV$, respectively. Here we take $c=1$, which means an attractive interaction between two particles. The initial condition I is taken.
• Figure 4: The coordinates and momentum of particle 1 (solid lines) and 2 (dashed lines). The black and red line represent the non-relativistic and relativistic evolution, respectively. Here we take $c=1$, which means an attractive interaction between the two particles. The initial condition II is chosen with $P_{\rm tot}=0$.
• Figure 5: The coordinates and momenta of particles 1 (solid lines) and 2 (dashed lines). The red and blue lines represent the results for two different time constraints, Eq. \ref{['eq.const2']}, and Eq. \ref{['eq.timec2']}, respectively. Here we take an attractive interaction between the two particles ($c=1$). The initial condition I is chosen.