The Feynman principle for a Fermi system

Abstract

A scheme for representing vectors and matrices as functions of a certain abstract symbol $\lambda $ is set up: though $\lambda $ has no numerical significance, it is found to behave as if it were an eigenvalue of a certain singular matrix $\boldsymbol{\Lambda}$. The resulting 'eigensymbol' theory is developed and applied to the quantum theory of Fermi systems. It is shown how a Feynman principle for such systems may be formulated in analogy with the familiar Feynman principle for a system with canonical p and q. The results are illustrated by the case of a simple Fermi oscillator.