On the triviality of the lambda-phi-4 model : theoretical foundation and numerical verification of a new approach

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Type
Thesis
Author
Kuppan, Loganantham
Supervisor
Foong, See Kit
Abstract
The λφ4 model is conventionally used to explain the origin of mass of the elementary particles through Spontaneous Symmetry Breaking (SSB) phenomena. The triviality status of the λφ4 model with reflectional symmetry in 4-dimensional spacetime remains an open question despite attempts by several authors. In this thesis, we construct and establish a new approach to determine the triviality status of this λφ4 model based on an unpublished note by Professor Bryce DeWitt. This approach is non-perturbative in nature and requires the computation of the propagator, namely the 2-point connected correlation function. The computation of the propagator which involves multidimensional integrals is achieved by employing numerical simulations based on Monte Carlo methods. For the construction of this approach, the model in 2 dimensional Euclidean space is taken as a test ground. The continuum 2 dimensional space is discretised and the continuum limit is approached as the lattice spacing goes to zero and the system size goes to infinity. The approach presented in this thesis analyzes the parameter β, a measure of deviation from the free field propagator. The parameter β is found to be finite and non-zero. For the determination of the triviality status of the λφ4 model, the renormalized coupling constant is commonly studied in the continuum. A non-zero value implies non-triviality of the model. The result obtained in this thesis is consistent with the findings by previous authors: the λφ4 model in 2 dimensions is non-trivial. The constructed new approach can be employed to determine the triviality status of the λφ4 model in other dimensions.
Date Issued
2008
Call Number
QC174.45 Kup
Date Submitted
2008