Modified loop expansion for nuclear matter in a chiral model

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Abstract
We consider loop expansions for the chirally symmetric linear σ model. The conventional loop expansion is reviewed, and the tachyon problems due to the large attractive σπ and σσ couplings are investigated. We then study a modified loop expansion that sums the repulsive baryon loops to all orders at each order in meson loops. Renormalizability is explicitly demonstrated to modified one-loop order, which corresponds to the relativistic random-phase approximation. We show that tachyons present in the conventional loop expansion are avoided to a large extent, but ghosts arise due to the unphysical behavior of the vacuum loops in this field theory that is not asymptotically free. Implications and possible solutions to this problem are discussed.