ELECTROWEAK BUBBLES AND SPHALERONS

We consider nonperturbative solutions of the Weinberg-Salam model at finite temperature. We employ an effective temperature-dependent potential yielding a first-order phase transition. In the region of the phase transition, there exist two kinds of static, spherically symmetric solutions: sphalerons and bubbles. We analyze these solutions as functions of temperature. We consider the most general spherically symmetric fluctuations about the two solutions and construct the discrete modes in the region of the phase transition. Sphalerons and bubbles both possess a single unstable mode. We present simple approximation formulas for these levels.