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Vacuum decay in quantum field theory
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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.
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CALZETTA, Esteban A., ROURA CRUMOLS, Albert and VERDAGUER OMS, Enric. Vacuum decay in quantum field theory. Physical Review D. 2001. Vol. 64, num. 10, pags. 105008-1-105008-21. ISSN 0556-2821. [consulted: 16 of October of 2026]. Available at: https://hdl.handle.net/2445/12320