Foundations of Physics

, Volume 30, Issue 3, pp 463–474 | Cite as

Instantons and Asymmetric Vacua

  • Gerald V. Dunne
Article

Abstract

It is shown that with asymmetric classical vacua the quantum mechanical instanton approach to the energy splitting of degenerate states applies even though the degenerate state in one well is not the quantum mechanical ground state of that well. The instanton approach leads to the correct leading exponential behavior of the energy splitting ΔE, but the prefactor is much more difficult to compute due to the asymmetric nature of the fluctuation potential V″(φc(t)), which is in turn a direct consequence of the asymmetry of the two classical minima between which the instanton interpolates.

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REFERENCES

  1. 1.
    A. M. Polyakov, Nucl. Phys. B 120, 429 (1977).Google Scholar
  2. 2.
    S. Coleman, Aspects of Symmetry (Cambridge University Press, Cambridge, 1985).Google Scholar
  3. 3.
    R. Rajaraman, Solitons and Instantons (North-Holland, Amsterdam, 1982).Google Scholar
  4. 4.
    T. Schäfer and E. Shuryak, Rev. Mod. Phys. 70, 323 (1998).Google Scholar
  5. 5.
    E. Gildener and A. Patrascioiu, Phys. Rev. D 16, 423 (1977).Google Scholar
  6. 6.
    L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-Relativistic Theory) (Pergamon, Oxford, 1977),Sec. 50, problem 3.Google Scholar
  7. 7.
    Note that if k is odd, then 〈φL|L,k〉=0, so we should instead compute a transition amplitude from the first central peak of the wavefunction in the left-hand well rather than from the very center of the left-hand well.Google Scholar
  8. 8.
    See Appendices 1 and 2 in Ref. 2.Google Scholar
  9. 9.
    P. Morse and H. Feshbach, Methods of Theoretical Physics, Vol. II (McGraw-Hill, New York, 1953). See Section 12.3, but note that there is a factor of 1/4 missing in the last term of Eq. (12.3.25) for the bound state energies.Google Scholar
  10. 10.
    W. Furry, Phys. Rev. 71, 360 (1947). 474 DunneGoogle Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Gerald V. Dunne
    • 1
  1. 1.Department of PhysicsUniversity of ConnecticutStorrs

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