We present a fully relativistic calculation of the Δ-isobar self-energy and dressed propagator. The unitarity of the S-matrix of the one-pion loop diagram provides us with the possibility to calculate the imaginary part of the self-energy and then, taking into account the analytic properties, we use a dispersion relation to derive the real part. The real part is found to exhibit a significant energy dependence and may be responsible for an additional suppression of the Δ propagator in the far off-shell region. Both the conventional and gauge-invariant πNΔ vertices are used in the calculation. The derived Δ-isobar self-energy and dressed propagator can be used in the models of the nucleon–baryon interaction that include the box-type, but not crossed-type, two-pion exchange diagrams.

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