Baryon chiral perturbation theory with explicit (1232) degrees of freedom is considered. The most general interactions of pions, nucleons, and consistent with all underlying symmetries as well as with the constraint structure of higher-spin fields are constructed. By use of the extended on-mass-shell renormalization scheme, a manifestly Lorentz-invariant effective-field theory with a systematic power counting is obtained. As applications, we discuss the mass of the nucleon, the pion-nucleon σ term, and the pole of the propagator.

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The magnetic dipole moment of the ∆(1232) is calculated in the framework of manifestly Lorentzinvariant baryon chiral perturbation theory in combination with the extended on-mass-shell renormalization scheme. As in the case of the nucleon, at leading order both isoscalar and isovector anomalous magnetic moments are given in terms of two low-energy constants. In contrast to the nucleon case, at next-to-leading order the isoscalar anomalous magnetic moment receives a (real) loop contribution. Moreover, due to the unstable nature of the ∆(1232), at next-to-leading order the isovector anomalous magnetic moment not only receives a real but also an imaginary loop contribution.