2009/12/02 by Abouzeid M. Shalaby, Shalaby, Abouzeid M.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.0912.0304
10 pages, 1 figure. We corrected the error existing in the previous version (thanks to Hugh F. Jones) and show that the soliton is non-topological one as well as many other features have been outlined
arxiv created 2010/01/17 · arxiv updated 2010/02/08
In this work, we show that, for the iϕ3 scalar field theory, their exists a contradiction between the assumption that the field is real and the fact that the quantized as well as the classical fields have to satisfy the Klein-Gordon equation. In solving the Klein-Gordon equation for the theory under investigation, we realized that the field is a pure imaginary solitary wave which spoils out the non-Hermiticity of the theory. Thus, instead of being non-Hermitian, the iϕ3 scalar field theory is a kind of a Hermitian-Lee-Wick theory which suffers from the existence of the famous ghost states and instability problems. We applied a Canonical transformation to obtain a Non-Hermitian and non-PT-symmetric representation which leads to the invalidity of the previous trials in the literature to cure the ghost states problem. Moreover, the solitonic solution is a non-topological one which is a very strange result to appear for a one component field theory. To account for this strange result, we conjecture that the iϕ3 scalar field theory has an equivalent Hermitian and non-Lee wick theory that have a conserved Noether current.