Some problems on the renormalisation of non-polynomial lagrangias - Daniel, M; Daniel, M. (1972)
﻿ 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 x1 = x2 = x3. A model of a massive neutral pseudovector field, Wandmu;, coupled to a non-conserved fermion current, jandmu; = andpsi;andgamma;andmu;andgamma;5andpsi;, 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, and#x2112;1int = gandnbsp;: jandmu;Aandmu;andnbsp;:andnbsp;, together with a non-polynomial strictly localisable interaction of the form and#x2112;2int = andminus;m andpsi;andnbsp;: (exp[iandkappa;andgamma;5B] andminus; 1)andnbsp;: andpsi; which can be treated by the methods developed in PART I of this thesis; (Aandmu;, B) are the Stuckelberg components of the Wandmu; 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.