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Of course, the presence of some of the features required by relativistic field theories does not necessarily make a theory relativistically invariant. See for instance C. Mahaux,proceedings of this conference.
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Coester, F. (1981). Nuclear forces and nuclear matter including pions and isobars. In: Zabolitzky, J.G., de Llano, M., Fortes, M., Clark, J.W. (eds) Recent Progress in Many-Body Theories. Lecture Notes in Physics, vol 142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018139
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DOI: https://doi.org/10.1007/BFb0018139
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