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In-medium effective chiral lagrangians and the pion mass in nuclear matter

We argue that the effective pion mass in nuclear matter obtained from chiral effective lagrangians is unique and does not depend on off-mass-shell extensions of the pion fields as e.g. the PCAC choice. The effective pion mass in isospin symmetric nuclear matter is predicted to increase slightly with increasing nuclear density, whereas the effective time-like pion decay constant and the magnitude of the density-dependent quark condensate decrease appreciably. The in-medium Gell-Mann-Oakes-Renner relation as well as other in-medium identities are studied in addition. Finally, several constraints on effective lagrangians for the description of the pion propagation in isospin symmetric, isotropic and homogenous nuclear matter are discussed. (Talk presented at the workshop ``Hirschegg '95: Hadrons in Nuclear Matter'', Hirschegg, Kleinwalsertal, Austria, January 16-21, 1995)