The Standard Model of electroweak interactions permits a variety of non-topological solutions such as magnetic monopoles and Z-strings.\u00a0 It has been demonstrated that static Z-strings are unstable:\u00a0 if any were produced (in, say, a particle accelerator) they would decay rapidly.\u00a0 We will investigate the stability of oscillatory Z-strings.\u00a0<\/p>\n
\u00a0\u00a0\u00a0 A simple mechanical model that captures some key properties of the Z-string is that of a particle in a saddle-like potential.\u00a0 Although the static solution, that of the particle at rest on the \u201cseat\u201d of the saddle, is unstable (it rolls off), we have shown that oscillatory solutions exhibit bands of stability in the oscillatory amplitude parameter space.\u00a0 This mechanical system will be generalized to a classical field system, the so called \u2018kink\u2019 solution embedded in a U(1) theory.\u00a0 The properties of the mechanical and U(1) systems will be used for greater physical intuition in the determination of the stability of an oscillating Z-string in the more complicated electroweak theory.\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"
Michael Salem with Tanmay VachaspatiStability of Oscillatory Solutions in Field Theory<\/p>\n
The Standard Model of electroweak interactions permits a variety of non-topological solutions such as magnetic monopoles and Z-strings.\u00a0 It has been demonstrated that static Z-strings are unstable:\u00a0 if any were produced (in, say, a particle accelerator) they would decay rapidly.\u00a0 We will investigate the stability of oscillatory Z-strings.\u00a0<\/p>\n
\u00a0\u00a0\u00a0 A simple mechanical model that captures some key properties of the Z-string is that of a particle in a saddle-like potential.\u00a0 Although the static solution, that of the particle at rest on the \u201cseat\u201d of the saddle,<\/p>\n