QCD inequalities for the nucleon mass and the free energy of baryonic matter

Thomas D. Cohen

Published 2003-04-02, updated 2003-06-06Version 3

The positivity of the integrand of certain Euclidean space functional integrals implies that the free energy per unit volume for QCD with a baryon chemical potential $\mu_B$ (and zero isospin chemical potential) is greater than the free energy with isospin chemical potential $\mu_I = (2 \mu_B)/N_c$ (and zero baryon chemical potential). This relation implies a bound on the nucleon mass: there exists a particle X in QCD such that $M_N \ge (N_c m_X)/(2 I_X)$ where $m_X$ is the mass and of the particle and $I_X$ is its isospin.