Ward identities and vector-boson field theories

• Main Author: Leithead, William E.
• Published: University of Edinburgh 1976
• Subjects: 531.16
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.653808

The object of this thesis is to investigate, using Ward identities, two aspects of vector-boson field theories. The first is to examine, in detail, how the renormalisation counter-terms for gauge field theories are accommodated without destroying the symmetry or corresponding Ward identities. In Chapter One the wave function and coupling constant renormalisations are studied and in Chapter Two the mass renormalisations. The conclusion is that, although there is complete freedom of choice of subtraction points for the wave function and coupling constant, the mass renormalisations are not so clear and may be restricted depending on the theory. The second topic is the massive Yang-Mills Lagrangian. In Chapter Three, we investigate the Ward identities, and their implications, for the tree approximation. In Chapter Four, we develop the Ward identities to all orders. The massive Yang-Mills Lagrangian is shown to be identical to a Lagrangian with transverse vector-boson propagators and a compensating scalar Lagrangian with an infinite series of interactions. The Lagrangian is identical to that of Boulware which was developed in the path integral formalism. The Ward identity approach we use is shown to be equivalent to Veltman's in Chapter Five. Furthermore, it is shown that it is the S-matrices which are identical. In Chapter Six, other possible equivalent formalisms of the massive Yang-Mills Lagrangian are investigated. The formalism of Hsu & Sudarshan is shown to be for mixed spin-one spin-zero fields and not pure spin-one fields as required. Finally a formulation is discussed which, in conjunction with the dimensional regularisation scheme of 't. Hooft and Veltman, generates the identical S-matrix from Feynman rules which are renormalisable according to power-counting.