Quantization of Fields of Arbitrary Spin

Abstract

The search for relativistic field equations for
elementary particles of arbitrary spin is a long standing
problem of Quantum Field Theory. Although much work has been
done on relativistic field theories describing fields with
various mass-spin spectra, little has been done on picking
out those theories which are quantizable, that is, those for
which a particle interpretation exists which is consistent
with the basic postulates of quantum theory.
In this thesis we examine theories based on the
relativistic field equation

(Lμϑμ + X)Ψ = 0.

The condition for ecahi tata on is expressed in terms of certain
positive definiteness requirements on the eigenvectors corresponding
to the non-zero eigenvalues of Lo. By restricting the.
discussion to a specific type of theory, in which spin states
are not repeated, these positive definiteness requirements are
expressed in terms of certain simple trace conditions. A
systematic procedure for finding representations of lo for
quantizable theories is given, and illustrated in the case of
spin 0,1,2 fields. In this procedure use is made of graphs
depicting the representations of the Lorentz Group according
to which % transforms ina relativistic field theory. Some
simple results of graph theory are applied to develop the theory
and also to discuss the properties of the Lo matrix. Further
possibilities of this graphical approach are briefly discussed.

Date of Award	1972
Original language	English