Quantization of Fields of Arbitrary Spin


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.

Additional Information: Copyright © Cox, 1972. B. Cox asserts their moral right to be identified as the author of this thesis. This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without appropriate permission or acknowledgement. If you have discovered material in Aston Publications Explorer which is unlawful e.g. breaches copyright, (either yours or that of a third party) or any other law, including but not limited to those relating to patent, trademark, confidentiality, data protection, obscenity, defamation, libel, then please read our Takedown Policy and contact the service immediately.
Institution: Aston University
Uncontrolled Keywords: Quantization,fields,arbitrary spin
Last Modified: 08 Dec 2023 08:01
Date Deposited: 09 Dec 2010 13:34
Completed Date: 1972
Authors: Cox, Bill

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