A new valley method for instanton deformation

Aoyama, Hideaki; Kikuchi, Hisashi

doi:10.1016/0550-3213(92)90384-n

Cited by 32 publications

(42 citation statements)

References 16 publications

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“…We use the following equation as a precise definition of the valley [7]: More important is the fact that with this definition, the eigenvalue λ of the second derivative of S is removed from the loop integrations. Initially, we separate the integration along the valley line from the whole functional integration.…”

Section: The Valley Methodsmentioning

confidence: 99%

“…The Gaussian integration is performed in the subspace defined by φ(τ )G i (τ )dτ = 0 for i = 1, · · · , D [7], where G j is the normalized function of F i . The Jacobian of the collective coordinate volume element i da i is given by the determinant of…”

Section: A Some Notes On the Valley Methodsmentioning

confidence: 99%

“…In Section 2, following Refs. [7,8,9, 10], we review a method to define the valleys in the configuration space and present the construction of the valley configurations and their basic constituents, the valley-instantons. Section 3 is the core of this paper; we will give a detailed analysis of a valley that contains a pair consisting of an instanton and an anti-instanton, and show that the interplay between the perturbative effects and the tunneling effects can be summarized in a unified way in terms of the collective coordinate of the valley.…”

Section: Introductionmentioning

confidence: 99%

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Valley views: instantons, large order behaviors, and supersymmetry

et al. 1999

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The elucidation of the properties of the instantons in the topologically trivial sector has been a long-standing puzzle. Here we claim that the properties can be summarized in terms of the geometrical structure in the configuration space, the valley. The evidence for this claim is presented in various ways. The conventional perturbation theory and the non-perturbative calculation are unified, and the ambiguity of the Borel transform of the perturbation series is removed. A 'proof' of Bogomolny's "trick" is presented, which enables us to go beyond the dilute-gas approximation. The prediction of the large order behavior of the perturbation theory is confirmed by explicit calculations, in some cases to the 478-th order. A new type of supersymmetry is found as a by-product, and our result is shown to be consistent with the non-renormalization theorem. The prediction of the energy levels is confirmed with numerical solutions of the Schrödinger equation.

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Section: The Valley Methodsmentioning

confidence: 99%

Section: A Some Notes On the Valley Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Valley views: instantons, large order behaviors, and supersymmetry

et al. 1999

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“…The essence of the improvement is the use of the proper valley method, which was developed independently by Silvestrov [9] and two of the present authors [10]. It teaches us how to enlarge the set of background configurations besides the classical solutions in order to take into account the global structure of the functional space.…”

Section: Introductionmentioning

confidence: 99%

Fake Instability in the Euclidean Formalism of Quantum Tunneling

Aoyama¹,

Harano²,

Kikuchi³

et al. 1997

Phys. Rev. Lett.

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We study the path-integral formalism in the imaginary-time to show its validity in a case with a metastable ground state. The well-known method based on the bounce solution leads to the imaginary part of the energy even for a state that is only metastable and has a simple oscillating behavior instead of decaying. Although this has been argued to be the failure of the Euclidean formalism, we show that proper account of the global structure of the path-space leads to a valid expression for the energy spectrum, without the imaginary part. For this purpose we use the proper valley method to find a new type of instanton-like configuration, the "valley instantons". Although valley instantons are not the solutions of equation of motion, they have dominant contribution to the functional integration. A dilute-gas approximation for the valley instantons is shown to lead to the energy formula. This method extends the well-known imaginary-time formalism so that it can take into account the global behavior of the theory.

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“…Since then, a lot of modifications of their calculations have been made [4], trying to solve the unitarity bound problem and to apply them to the case at the energy above the Sphaleron. Among them, the valley method [5,6,7,8,9] showed an optimistic result suggesting that the anomalous cross section reaches an observable one without breaking the unitarity bound at the energy of the order of E sp (∼ 10Tev) [8]. In this method, total cross section σ tot in the instanton background (I) is computed, via optical theorem, as the imaginary part of the forward elastic scattering amplitude (ℑ(F ES)) in the instantonanti-instanton background(I-Ī),…”

Section: Introductionmentioning

confidence: 99%

Fermion Modes in Instanton-Anti-Instanton Background in (1 + 0)-Dimensional Model

Aoki

1994

Progress of Theoretical Physics

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We evaluate the eigenvalues of Dirac operator in the background of instanton-antiinstanton configuration (I-Ī), in a simple (1+0)-dimensional model, and find that quasizero-mode disappears for the closely localized I-Ī configurations. This result suggests that the configurations which are dominant at high energy in the valley method are actually non-anomalous ones and irrelevant to fermion number violation. Hence, there seems to be no theoretical basis for expecting anomalous cross section to become observable at energies of 10 Tev region in Weinberg-Salam theory.

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A new valley method for instanton deformation

Cited by 32 publications

References 16 publications

Valley views: instantons, large order behaviors, and supersymmetry

Valley views: instantons, large order behaviors, and supersymmetry

Fake Instability in the Euclidean Formalism of Quantum Tunneling

Fermion Modes in Instanton-Anti-Instanton Background in (1 + 0)-Dimensional Model

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