Vacuum decay in quantum field theory

ALBERT ROURA; ENRIC VERDAGUER; ESTEBAN CALZETTA

PHYSICAL REVIEW D - PARTICLE AND FILDS

APS

Año: 2001 vol. 64 p. 1 - 21

0556-2821

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size M−1. This effect makes a substantial contribution to the total decay rate.