We present a consistent picture of tunnelling in field theory. Our results apply both to high-temperature field theories in four dimensions and to zero-temperature three-dimensional ones. Our approach is based on the notion of a coarse-grained potential U-k that incorporates the effect of fluctuations with characteristic momenta above a given scale k. U-k is non-convex and becomes equal to the convex effective potential for k --> 0. We demonstrate that a consistent calculation of the nucleation rate must be performed at non-zero values of k, larger than the typical scale of the saddle-point configuration that dominates tunnelling. The nucleation rate is exponentially suppressed by the action S-k Of this Saddle point. The pre-exponential factor A(k), which includes the fluctuation determinant around the saddle-point configuration, is well-defined and finite. Both S-k and A(k) are k-dependent, but this dependence cancels in the expression for the nucleation rate. This picture breaks down in the limit of very weakly first-order phase transitions, for which the pre-exponential factor compensates the exponential suppression. (C) 1999 Elsevier Science B.V.

A consistent calculation of bubble-nucleation rates

STRUMIA, ALESSANDRO;
1999-01-01

Abstract

We present a consistent picture of tunnelling in field theory. Our results apply both to high-temperature field theories in four dimensions and to zero-temperature three-dimensional ones. Our approach is based on the notion of a coarse-grained potential U-k that incorporates the effect of fluctuations with characteristic momenta above a given scale k. U-k is non-convex and becomes equal to the convex effective potential for k --> 0. We demonstrate that a consistent calculation of the nucleation rate must be performed at non-zero values of k, larger than the typical scale of the saddle-point configuration that dominates tunnelling. The nucleation rate is exponentially suppressed by the action S-k Of this Saddle point. The pre-exponential factor A(k), which includes the fluctuation determinant around the saddle-point configuration, is well-defined and finite. Both S-k and A(k) are k-dependent, but this dependence cancels in the expression for the nucleation rate. This picture breaks down in the limit of very weakly first-order phase transitions, for which the pre-exponential factor compensates the exponential suppression. (C) 1999 Elsevier Science B.V.
1999
Strumia, Alessandro; Tetradis, N.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/169185
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 42
social impact