Vacuum Transitions in Field Theory: Insights and Approaches

Understanding vacuum transitions in field theory is crucial in theoretical physics. Various approaches have been explored, from the WKB decay interpretation to newer methods such as the direct approach and Lorentzian approach. References to key works by notable physicists provide a comprehensive overview of the field.

• Field Theory
• Vacuum Transitions
• Theoretical Physics
• Quantum Field Theory

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1. VACUUM TRANSITIONS IN FIELD THEORY Christopher Hughes DAMTP, University of Cambridge Supported by: NUI Travelling Doctoral Studentship Robert Gardiner Memorial Scholarship

2. EUCLIDEAN APPROACH 1. WKB suggests the decay is given by Equivalent to Bounce solution of negative potential What is wrong with this?

3. EUCLIDEAN APPROACH 2. Decay given by imaginary part of the partition function (at large times) But Z will be real for physical (bounded from below) potentials Need to deform contour to integrate over saddle points

4. NEWER APPROACHES Schwartz et al. (2016/7/8) Direct Approach An equivalent formulation using propagators that does not require analytic continuation of the potential. Applied to the Higgs potential to estimate the lifetime of the universe . Quevedo et al. (2020) Lorentzian Approach Works in Lorentzian time via a Hamiltonian approach. Allows both open and closed universes from a decay of the cosmological constant.

5. REFERENCES S. R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D, vol. 15,pp. 2929 2936, 1977. [Erratum: Phys.Rev.D 16, 1248 (1977)]. C. G. Callan and S. Coleman, Fate of the false vacuum. ii. first quantum corrections, Phys. Rev.D, vol. 16, pp. 1762 1768, Sep 1977 S. R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D,vol. 21, p. 3305, 1980. A. Andreassen, D. Farhi, W. Frost and M. D. Schwartz, Precision decay Rate Calculations in Quantum Field Theory, Phys. Rev. D, vol 95, 2017 A. Andreassen, W. Frost, and M. D. Schwartz, Scale-invariant instantons and the complete life-time of the standard model, Physical Review D, vol. 97, Mar 2018 S. Cespedes, S. P. de Alwis, F. Muia and F. Quevedo, Lorentzian Vacuum Transitions: Open or Closed Universes? [arXiv:2011.13936 [hep-th]]