## Topics in quantum field theory

##### Abstract

The subject matter of this thesis falls into two distinct
parts. Chapters II to IV are devoted to a discussion of
Schwinger's action principle, and chapters V and VI are
concerned with the proof of dispersion relations for
inelastic meson-nucleon scattering.
The material of chapter II is based on some work done
in collaboration with Dr. J.C. Polkinghorne, which has been
published (Kibble and Polkinghorne 1957). This work was
concerned with the clarification of certain points connected
with the class of permissible variations in Schwinger's
principle. There are, however, substantial changes in the
present treatment, principally deriving from the introduction,
in section II-5, of the concept of relative phases. This
chapter is restricted to the case of non-relativistic
quantum theory, and the discussion is extended to
relativistic quantum field theory in chapter III. These
chapters are devoted to a reformulation of Schwinger's
action principle, and an investigation of the consequences
of the new form of the action principle. Some of this
material is necessarily contained in the work of Schwinger
(1951, 1953a), but the treatment differs from his in several
important respects. These are discussed in greater detail in section 2.
Chapter IV is devoted to a discussion of higher order
spinor Lagrangians, with particular reference to the use of
a two-component field satisfying a second-order equation
rather than a four-component spinor satisfying a first-order
equation. This procedure has been suggested by Feynman
and Gell-Mann (1958) in connection with their universal Fermi
interaction. The work presented in this chapter was done
jointly with Dr. J.C. Polkinghorne, and has been published
(Kibble and Polkinghorne 1958).
Chapters V and VI are devoted to a proof of the
dispersion relations for the process in which a single meson
is scattered on a nucleon into a state with several mesons.
The proof follows the general lines of that by Bogolyubov,
Medvedev and Polivanov (1956) for the case of elastic
meson-nucleon scattering, This work has also been published (Kibble 1958).
The notation employed in the thesis is summarized in
appendix A. Appendix B is devoted to a discussion of
consistency conditions on the Lagrangian function.
The chapter number is omitted in references to sections
or equations, except in the case of cross references between
chapters.