One-loop corrections to the instanton transition in the Abelian Higgs model: Gel’fand-Yaglom and Green’s function methods

Baacke, Juergen

doi:10.1103/physrevd.78.065039

Cited by 14 publications

(6 citation statements)

References 33 publications

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“…To obtain the functional determinants, we follow e.g., Refs. [16,[27][28][29] and generalize the Green's functions M X;k ðφ; z; z 0 Þ to resolvents…”

Section: B Green's Function Methodsmentioning

confidence: 99%

Gradient effects on false vacuum decay in gauge theory

Cruz

Garbrecht

et al. 2020

Phys. Rev. D

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We study false vacuum decay for a gauged complex scalar field in a polynomial potential with nearly degenerate minima. Radiative corrections to the profile of the nucleated bubble as well as the full decay rate are computed in the planar thin-wall approximation using the effective action. This allows to account for the inhomogeneity of the bounce background and the radiative corrections in a self-consistent manner. In contrast to scalar or fermion loops, for gauge fields one must deal with a coupled system that mixes the Goldstone boson and the gauge fields, which considerably complicates the numerical calculation of Green's functions. In addition to the renormalization of couplings, we employ a covariant gradient expansion in order to systematically construct the counterterm for the wave-function renormalization. The result for the full decay rate however does not rely on such an expansion and accounts for all gradient corrections at the chosen truncation of the loop expansion. The ensuing gradient effects are shown to be of the same order of magnitude as nonderivative one-loop corrections.

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“…To obtain the functional determinants, we follow e.g., Refs. [16,[27][28][29] and generalize the Green's functions M X;k ðφ; z; z 0 Þ to resolvents…”

Section: B Green's Function Methodsmentioning

confidence: 99%

Gradient effects on false vacuum decay in gauge theory

Cruz

Garbrecht

et al. 2020

Phys. Rev. D

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“…In this section, we compute the ratio of functional determinants. To do so, we employ the resolvent method, developed in [24][25][26][27] and used in, e.g., [17,[28][29][30]. The method states that the ratio of the determinants of two operators can be written as an integral of some modified Green's function.…”

Section: The Tunneling Contributionmentioning

confidence: 99%

Double-well instantons in finite volume

Ai,

Alexandre,

Carosi

et al. 2024

J. High Energ. Phys.

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Assuming a toroidal space with finite volume, we derive analytically the full one-loop vacuum energy for a scalar field tunnelling between two degenerate vacua, taking into account discrete momentum. The Casimir energy is computed for an arbitrary number of dimensions using the Abel-Plana formula, while the one-loop instanton functional determinant is evaluated using the Green’s functions for the fluctuation operators. The resulting energetic properties are non-trivial: both the Casimir effect and tunnelling contribute to the Null Energy Condition violation, arising from a non-extensive true vacuum energy. We discuss the relevance of this mechanism to induce a cosmic bounce, requiring no modified gravity or exotic matter.

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“…The method for calculating the fluctuation determinants based on the resolvent has been applied to tunneling problems in Refs. [37,[50][51][52][53]. We consider the following eigenvalue equations where i = 1, 2 and s ∈ R is an auxiliary parameter.…”

Section: B2 Integration Over the Resolventmentioning

confidence: 99%

Functional methods for false-vacuum decay in real time

Garbrecht

Tamarit

2019

J. High Energ. Phys.

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We present the calculation of the Feynman path integral in real time for tunneling in quantum mechanics and field theory, including the first quantum corrections. For this purpose, we use the well-known fact that Euclidean saddle points in terms of real fields can be analytically continued to complex saddles of the action in Minkowski space. We also use Picard-Lefschetz theory in order to determine the middle-dimensional steepest-descent surface in the complex field space, constructed from Lefschetz thimbles, on which the path integral is to be performed. As an alternative to extracting the decay rate from the imaginary part of the ground-state energy of the false vacuum, we use the optical theorem in order to derive it from the real-time amplitude for forward scattering. While this amplitude may in principle be obtained by analytic continuation of its Euclidean counterpart, we work out in detail how it can be computed to one-loop order at the level of the path integral, i.e. evaluating the Gaußian integrals of fluctuations about the relevant complex saddle points. To that effect, we show how the eigenvalues and eigenfunctions on a thimble can be obtained by analytic continuation of the Euclidean eigensystem, and we determine the path-integral measure on thimbles. This way, using real-time methods, we recover the one-loop result by Callan and Coleman for the decay rate. As a byproduct of our derivation, we note that the optical theorem suggests an interpretation of the false-vacuum energy in flat space in terms of the normalization of the position or field eigenstate associated with the false vacuum, with unit norm corresponding to zero energy up to volume-suppressed effects. We finally demonstrate our real-time methods explicitly, including the construction of the eigensystem of the complex saddle, on the archetypical example of tunneling in a quasi-degenerate quartic potential. arXiv:1905.04236v1 [hep-th]

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One-loop corrections to the instanton transition in the Abelian Higgs model: Gel’fand-Yaglom and Green’s function methods

Cited by 14 publications

References 33 publications

Gradient effects on false vacuum decay in gauge theory

Gradient effects on false vacuum decay in gauge theory

Double-well instantons in finite volume

Functional methods for false-vacuum decay in real time

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