Michael Salem with Tanmay Vachaspati

Stability of Oscillatory Solutions in Field Theory

The Standard Model of electroweak interactions permits a variety of non-topological solutions such as magnetic monopoles and Z-strings.  It has been demonstrated that static Z-strings are unstable:  if any were produced (in, say, a particle accelerator) they would decay rapidly.  We will investigate the stability of oscillatory Z-strings. 

    A simple mechanical model that captures some key properties of the Z-string is that of a particle in a saddle-like potential.  Although the static solution, that of the particle at rest on the “seat” of the saddle, is unstable (it rolls off), we have shown that oscillatory solutions exhibit bands of stability in the oscillatory amplitude parameter space.  This mechanical system will be generalized to a classical field system, the so called ‘kink’ solution embedded in a U(1) theory.  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.