Nucleation at finite temperature beyond the superminispace model

Abstract

The transition from the quantum to the classical regime of the nucleation of the closed Robertson-Walker Universe with spacially homogeneous matter fields is investigated with a perturbation expansion around the sphaleron configuration. A criterion is derived for the occurrence of a first-order type transition, and the related phase diagram for scalar and vector fields is obtained. For scalar fields both the first and second order transitions can occur depending on the shape of the potential barrier. For a vector field, here that of an O(3) nonlinear $\sigma$-model, the transition is seen to be only of the first order.Comment: 15 pages, 3 figure

Tunneling of Born–Infeld strings to D2-branes

“…[9] and [10]). In the present case the vacuum solution has C = D, and the sphaleron C = (1 + h 2 D 2 )/2h.…”

“…Further applications of the criterion have been given in refs. [9] and [10]. The criterion for occurrence of a first order transition is Ω 2 − Ω 2 S > 0, where Ω S is the sphaleron frequency and Ω the possible frequency different from Ω S [8].…”

“…We now consider the general solution of the static equation (10). Assuming R − ≤ R ≤ R + and R(z 0 ) = R + , eq.…”

“…With the formulas at hand we can now plot the phase diagrams.The integration constant C here plays the same role as the energy E of a pseudoparticle in the usual quantum mechanics around such a configuration (E = 0 in the latter being its value for the vacuum solution, and E = E sph that for the sphaleron, see e.g. [9] and [10]). In the present case the vacuum solution has C = D, and the sphaleron C = (1 + h 2 D 2 )/2h.…”