Kaon Zero-Point Fluctuations in Neutron Star Matter

We investigate the contribution of zero-point motion, arising from uctuations in kaon modes, to the ground state properties of neutron star matter containing a Bose condensate of kaons. The zero-point energy is derived via the thermodynamic partition function, by integrating out uctuations for an arbitrary value of the condensate eld. It is shown that the vacuum counterterms of the chiral Lagrangian ensure the cancellation of divergences dependent on , the charge chemical potential, which may be regarded as an external vector potential. The total grand potential, consisting of the treelevel potential, the zero-point contribution, and the counterterm potential, is extremized to yield a locally charge neutral, beta-equilibrated and minimum energy ground state. In some regions of parameter space we encounter the well-known problem of a complex e ective potential. Where the potential is real and solutions can be obtained, the contributions from uctuations are