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Quantization of an interacting spin-3/2 field and the Delta isobar

V. Pascalutsa
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Abstract

Quantization of the free and interacting Rarita-Schwinger field is considered using the Hamiltonian path-integral formulation. The particular interaction we study in detail is the $πN \De$ coupling used in the phenomenology of the pion-nucleon and nucleon-nucleon systems. Within the Dirac constraint analysis, we show that there is an excess of degrees of freedom in the model, as well as the inconsistency related to the Johnson-Sudarshan-Velo-Zwanzinger problem. It is further suggested that couplings invariant under the gauge transformation of the Rarita-Schwinger field are generally free from these inconsistencies. We then construct and briefly analyse some lowest in derivatives gauge-invariant $πN \De$ couplings.

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V. Pascalutsa. 1998-09-18. Quantization of an interacting spin-3/2 field and the Delta isobar. https://doi.org/10.1103/physrevd.58.096002

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