| Summary: | A method of analytic renormalisation is developed (in PART I of the thesis) to define the three point time ordered product of massless fields of exponential type as a strictly localisable distribution in the Jaffe Class. The uniqueness property, known for the two point T-product, is verified for the three point T-product for a special choice of finite renormalisation. It is characterised by minimum singularity on the 'light cone' (the Lehraann-Pohlmeyer 'ansatz'); there are no delta function type singularities concentrated on the point x<sub>1</sub> = x<sub>2</sub> = x<sub>3</sub>. A model of a massive neutral pseudovector field, W<sub>μ</sub>, coupled to a non-conserved fermion current, j<sub>μ</sub> = ψγ<sub>μ</sub>γ<sub>5</sub>ψ, is considered (in PART II of the thesis). The generalised Stuckelberg formalism is used to convert the above non-renormalisable coupling into a conventionally renormalisable interaction, together with a non-polynomial strictly localisable interaction which can be treated by the methods developed in PART I of this thesis; (A<sub>μ</sub>, B) are the Stuckelberg components of the W<sub>μ</sub> field, and the B is taken to be a massless pseudoscalar field giving, thus, rise to massless 'superpropagators'. The renormalisation of the model theory is effected with the help of generalised Ward-Takahashi identities by adding suitable gauge invariant counterterms in the original interaction Lagrangian to cancel out the infinities of the theory. Thus the complete theory becomes renormalisable.
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