The triviality and non-triviality of Lambda-Phi-4 model in different spacetime dimensions
Foong, See Kit.
Date of Issue2011
National Institute of Education
Our research is an attempt to resolve the triviality status of the Lambda-PHI-4 model in 4-dimensions. The dynamics of the real valued scalar field PHI of the Lambda-PHI-4 model in d-dimensional Euclidean space is described by the action SE[PHI]=Integration(d^(d)x(1/2(deluPHI)^2+1/2m^2PHI^2+1/4!LambdaPHI^4) where m^2 and lambda are the bare mass and bare coupling constant respectively. Because of the close resemblance between this Lambda-PHI-4 model and the Higgs model,the triviality status of this model, that is, whether the field PHI self-interact or behaves like a free field has been of much interest. It is known that the Lambda-PHI-4 model is trivial in dimensions more than 4 and non-trivial in dimensions less than 4.However,in 4-dimensions, the triviality status of this model is not known decisively .