The S-matrix: From Heisenberg Till Now

Abstract

This chapter takes an in-depth look at the concept of S-matrix. It starts with an elaborate analysis of Heisenberg’s introduction and his initial motivations, along with Pauli’s criticisms. It describes how Heisenberg’s initial program of shifting emphasis to only observable aspects, augmented by Lorentz Invariance and some minimal analyticity grew with subsequent inclusion of causality, crossing-symmetry, etc. It takes a detailed look at Heisenberg’s initial papers. The dramatic suggestion of Kronig to include causality is explained in detail along with the works of Kronig and Kramers that motivated it. The connection between causality and analyticity, which was a hallmark of the Kramers-Kronig works is explained lucidly, and in considerable depth. After explaining how this connection works in non-relativistic Quantum Mechanics, the stage is set for the analogous discussion in Relativistic Quantum Field Theory(RQFT) based on the concept of microcausality. The nuances of this concept with regard to issues of measurability of quantum fields, particularly the fermionic and gauge fields are also clarified. Forty references covering the period 1937–1957 including many book references are included to aid the readers.