Vacuum stability and vacuum excitation in a spin-0 field theory

Abstract

The theoretical possibility that in a limited domain in space the expectation value $〈\ensuremath{\varphi}(x)〉$ of a neutral spin-0 field may be abnormal (that is to say quite different from its normal vacuum expectation value) is investigated. It is shown that if the ${\ensuremath{\varphi}}^{3}$ coupling is sufficiently large, then such a configuration can be metastable, and its physical size may become substantially greater than the usual microscopic dimension in particle physics. Furthermore, independent of the strength of the ${\ensuremath{\varphi}}^{3}$ coupling, if $\ensuremath{\varphi}(x)$ has sufficiently strong scalar interaction with the nucleon field, the state that has an abnormal $〈\ensuremath{\varphi}(x)〉$ inside a very heavy nucleus can become the minimum-energy state, at least within the tree approximation; in such a state, the "effective" nucleon mass inside the nucleus may be much lower than the normal value. Both possibilities may lead to physical systems that have not yet been observed.