Pion-Nucleon Scattering in Kadyshevsky Formalism and Higher Spin Field Quantization

TL;DR

This thesis develops a covariant, causal approach to pion-nucleon scattering using Kadyshevsky formalism and advances higher spin field quantization with auxiliary fields, addressing issues of contact terms and covariance.

Contribution

It introduces a method to cancel unwanted contact terms in Kadyshevsky formalism and presents a full constraint analysis for higher spin fields with covariant propagators.

Findings

Tree level amplitudes are causal, covariant, and n-independent.

Amplitudes are half of the Feynman expressions, containing only positive energy states.

Auxiliary fields yield covariant propagators for higher spin fields.

Abstract

This thesis contains two parts. The first part deals with pion-nucleon/meson-baryon scattering in the Kadyshevsky formalism. This formalism is introduced and discussed. Problems may arise when derivative couplings and/or higher spin fields are used, especially when compared to the results in the Feynman formalism: unwanted contact terms pop-up. These terms are cancelled using the Gross and Jackiw or Takahashi and Umezawa method. The final results in both formalisms are therefore equal, causal and covariant. Formal incorporation of pair suppression in the baryon exchange sector is achieved using a method based on the Takahashi and Umezawa method. For the resulting tree level amplitudes, we have shown, to our knowledge for the first time, that they are causal, covariant and n-independent. Moreover, the amplitudes are just a factor 1/2 of the usual Feynman expressions. The amplitudes contain only posititve energy initial and final states, although it should be mentioned that negative energy is present inside an amplitude via the Delta propagator. The second part of this thesis deals with higher spin field quantization in the framework of Dirac's Constraint analysis. A full constraint analysis and quantization procedure is presented for the free spin 1,3/2 and 2 case and for the situation where these fields are coupled to auxiliary fields. The constructed propagators in the former case are shown to be non-covariant, as is well-known. Therefore, auxiliary fields coupled to gauge conditions of the free case are introduced in the Lagrangian. Now, the resulting propagators are covariant.