Vacuum Polarization Energy of the Kinks in the Sinh-Deformed Models

Takyi, I.; Barnes, Belinda; Ackora-Prah, Joseph

doi:10.48550/arxiv.2012.12343

Cited by 2 publications

(3 citation statements)

References 35 publications

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“…Given a stationary kink solution, one may compute its normal modes and even their interactions [31]. Every year, this is done for new classes of models [32][33][34], including recently even gravitating kinks [35,36]. With these normal modes in hand, one can construct the quantum states corresponding to kinks.…”

Section: Remarksmentioning

confidence: 99%

A reduced inner product for kink states

Evslin

Liu

2023

J. High Energ. Phys.

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Solitons in classical field theories correspond to states in quantum field theories. If the spatial dimension is infinite, then momentum eigenstates are not normalizable. This leads to infrared divergences, which are generally regularized via wave packets or by compactification. However, in some applications both possibilities are undesirable. In the present note, we introduce a finite inner product on translation-invariant kink states that allows us to compute probabilities involving these nonnormalizable states. Essentially, it is the quotient of the usual inner product by the translation group. We present a surprisingly simple formula for the reduced inner product, which requires no knowledge of the zero-mode dependence of the states but includes a correction which accounts for the mixing between zero modes and normal modes as the kink moves. As an application, we show that initial and final state corrections to meson multiplication vanish. However, we find that the pole of the subleading term in the initial state requires an infinitesimal imaginary shift.

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Section: Remarksmentioning

confidence: 99%

A reduced inner product for kink states

Evslin

Liu

2023

J. High Energ. Phys.

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“…The second term can be decomposed into the contributions µ (20) and µ (21) in which the dummy index is the shape mode or a continuum mode respectively…”

Section: Energy Required To Excite a Shape Modementioning

confidence: 99%

“…Recently, in Ref. [20] (see also [21,22]), a number of new examples of such bound excitations have been found, and an efficient algorithm was described for generating them. Our method can only be applied to stable kinks, as we require Hamiltonian eigenstates, but using the stability criterion in Refs.…”

Section: Continuum Thresholdmentioning

confidence: 99%

Evidence for the Unbinding of the $ϕ^4$ Kink's Shape Mode

Evslin

2021

Preprint

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The φ 4 double-well theory admits a kink solution, whose rich phenomenology is strongly affected by the existence of a single bound excitation called the shape mode. We find that the leading quantum correction to the energy needed to excite the shape mode is −0.115567λ/m in terms of the coupling λ/4 and the meson mass m evaluated at the minimum of the potential. On the other hand, the correction to the continuum threshold is −0.433λ/m. A naive extrapolation to finite coupling then suggests that the shape mode melts into the continuum at the modest coupling of λ/4 ∼ 0.106m 2 , where the Z 2 symmetry is still broken.

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Vacuum Polarization Energy of the Kinks in the Sinh-Deformed Models

Cited by 2 publications

References 35 publications

A reduced inner product for kink states

A reduced inner product for kink states

Evidence for the Unbinding of the $ϕ^4$ Kink's Shape Mode

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