Relation between tunneling and particle production in vacuum decay

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 59, Issue 12, 1999, Pages

  Mersini, Laura ^a  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85037898639     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.59.123521     Document Type: Article

References (27)

1. S. Coleman, Phys. Rev. D 15, 2929 (1977);
2. Phys. Rev. DS. Coleman16, 1248(E) (1977);
3. Phys. Rev. DC.G. Callan and S. Coleman, 16, 1762 (1977).
4. J.L. Gervais and B. Sakita, Phys. Rev. D 16, 3507 (1977).
5. H.J. Vega, J.L. Gervais, and B. Sakita, Phys. Rev. D 19, 604 (1979).
6. V.A. Rubakov, Nucl. Phys. B245, 481 (1984).
7. T. Banks, C. Bender, and T.T. Wu, Phys. Rev. D 8, 3366 (1973).
8. T. Vachaspati and A. Vilenkin, Phys. Rev. D 37, 898 (1988).
9. T. Vachaspati and A. Vilenkin, Phys. Rev. D 43, 3846 (1991).
10. M. Sasaki and T. Tanaka, Phys. Rev. D 49, 1039 (1994).
11. S. Hamazaki, M. Sasaki, T. Tanaka, and K. Yamamoto, Phys. Rev. D 53, 2045 (1995).
12. E. Keski-Vakkuri and Per Krauss, Phys. Rev. D 54, 7607 (1996).
13. L. Parker, Phys. Rev. D 183, 1057 (1969).
14. L. Parker, Nature (London) 261, 20 (1976).
15. B.K. Berger, Phys. Rev. D 12, 368 (1975).
16. W.G. Unruh, Phys. Rev. D 14, 870 (1976).
17. B.L. Hu, Phys. Rev. D 9, 3263 (1974).
18. L. Parker, in Asymptotic Structure of Space-Time, edited by F.P. Esposito and L. Witten (Plenum, New York, 1977).
19. B.L. Hu and D.J. O’Connor, Phys. Rev. D 36, 1701 (1987).
20. B.L. Hu, Class. Quantum Grav. 10, 593 (1993).
21. S. Coleman, V. Glaser, and A. Martin, Commun. Math. Phys. 58, 211 (1978).
22. Handbook of Mathematical Functions, edited by M. Abramovitz and A. Stegum (Dover, New York, 1985).
23. Quantum Fields in Curved Space, edited by N.D. Birrel and P.C.W. Davies, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 1982).
24. More commonly known as the bounce solution, i.e., the solution for (Formula presented) under the barrier that interpolates between the two values of (Formula presented) for the false and true vacuum.
25. Since there is one integration constant (the wall of the bubble) the wave-functional ψ is peaked around a 1-parameter family of solutions (Formula presented) where the s-parameter is taken to be the integration constant in the solution for σ.
26. There is no Cauchy surface in Milne Universe to cover the whole of Minkowski space. For subtleties related to that (e.g., discrete modes) see 9. We will not mention those in this paper as they do not affect our result.
27. This interpretation is based on the analogy between the Euclidean path integral of QFT and the partition function in statistical mechanics, i.e., finding the time evolution of the field is equivalent to summing up over the ensemble of instantons. The usefulness of taking this point of view will become clearer in a following paper (L. Mersini, “Finite temperature resonant tunneling in false vacuum decay and the Lee-Yang Theorem”). That interpretation sets the stage that allows us to extend the above results to finite temperature by relying heavily on the analogy between the Euclidean path integral and partition functions of ferromagnets.