The gauge invariance,kinematical singularities and the electro- and photopion production amplitudes

The kinematical singularities connected with the gauge invariance are considered and the conventional sets of invariant amplitudes discussed. A new set of invariant amplitudes for electro-production of pions on nucleons is proposed, which contains the transversal subset of photo-production amplitudes, is free of kinematical singularities and more convenient for practical calculations.I would like to thank Dr. M. Petrá for a valuable discussion on some points, Dr. P. Lichard and Dr. J. Piút for useful remarks and Dr. F. A. Berends for a valuable correspondence. I am also indebted to Prof. Moorhouse for drawing my attention to some important papers and sending me a preprint of one of them.