Parity Doubling andSU(2)L×SU(2)RRestoration in the Hadron Spectrum

We construct the most general nonlinear representation of chiral $\mathrm{SU}(2{)}_L\times \mathrm{SU}(2{)}_R$ broken down spontaneously to the isospin SU(2), on a pair of hadrons of same spin and isospin and opposite parity. We show that any such representation is equivalent, through a hadron field transformation, to two irreducible representations on two hadrons of opposite parity with different masses and axial-vector couplings. This implies that chiral symmetry realized in the Nambu-Goldstone mode does not predict the existence of degenerate multiplets of hadrons of opposite parity nor any relations between their couplings or masses.