A method to obtain bounds on the equation of state of cold nuclear matter from imaginary chemical potentials

The sign problem in numerical calculations of the QCD Euclidean space path integral of QCD with a chemical potential vanishes if the chemical potential is imaginary. Moreover, calculations of the partition function with imaginary chemical potentials are equivalent to calculations with Lagrange multipliers enforcing the current density. At zero temperature, Lorentz boosts allow one to deduce properties of systems with both number density and current density from properties of systems with a current density alone; this allows both upper and lower bounds to be determined for the equation of state (EOS) in the form of energy density as a function of number density.

💡 Research Summary

The paper proposes a novel strategy to constrain the zero‑temperature equation of state (EOS) of cold nuclear matter by exploiting QCD calculations at imaginary chemical potential, where the notorious sign problem disappears. An imaginary baryon chemical potential μ = i μ_E in Minkowski space corresponds to a real Lagrange multiplier μ_E in Euclidean space that fixes the baryon number density. Moreover, the same Euclidean functional integral with a Lagrange multiplier λ_z that fixes a spatial current j_z is mathematically identical to the theory with an imaginary chemical potential of magnitude μ_E.

At T = 0 the system is Lorentz invariant, so a boost with velocity β along the direction of the current transforms the energy‑momentum tensor and the four‑current as

 T′_tt = (T_tt + β² T_zz)/(1 − β²), n′ = β j_z/(1 − β²), j′_z = j_z/(1 − β²).

Because the boosted configuration is a physical state, its energy density must be greater than or equal to the minimal energy density ϵ(n′) for the same baryon density n′. This observation yields an upper bound on ϵ(n):

 ϵ(n_u^β) ≤