arXiv subjects

Z. Shahbazi

Publications and source records attributed to Z. Shahbazi.

2 recordsLinked to original sources

arXiv2024

The modulated soliton fields in the Goldstone boson model

It is well known that massless Goldstone bosons have not yet been observed. In the Goldstone boson model, after the spontaneous symmetry breaking under $U(1)$, two coupled nonlinear equations are obtained for which we present the exact solitonic solutions. These solutions completely localize the energy density of the model and show the existence of two boson fields, one massive and the other massless. Also, it is seen that the solitonic waves are modulated and the massless wave rides on the massive wave. Finally, we calculate the charge density of the model, which again confirms the neutrality of these boson fields. Since massive bosons can be observed in the laboratory, these solitonic waves may be useful in tracking and detecting Goldstone bosons.

hep-th↗

arXiv2020

A conjecture of Cameron and Kiyota on sharp characters with prescribed values

Let $ χ$ be a virtual (generalized) character of a finite group $ G $ and $ L=L(χ)$ be the image of $ χ$ on $ G-\lbrace 1 \rbrace $. The pair $ (G, χ) $ is said to be sharp of type $ L $ if $|G|=\prod _{ l \in L} (χ(1) - l) $. If the principal character of $G$ is not an irreducible constituent of $χ$, the pair $(G,χ)$ is called normalized. In this paper, we first provide some counterexamples to a conjecture that was proposed by Cameron and Kiyota in $1988$. This conjecture states that if $(G,χ)$ is sharp and $|L|\geq 2$, then the inner product $(χ,χ)_G$ is uniquely determined by $ L $. We then prove that this conjecture is true in the case that $(G,χ) $ is normalized, $χ$ is a character of $ G $, and $ L $ contains at least an irrational value.

math.RT↗