Quantum Corrections to Solitons in the $Φ^8$ Model

Takyi, I.; Matfunjwa, M. K.; Weigel, H.

doi:10.48550/arxiv.2010.07182

Cited by 4 publications

(5 citation statements)

References 17 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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“…To illustrate this procedure, in Appendix A we find the leading correction in the case of the φ 4 double well and show that it is exponentially small in Λ/m. 4 The Kink Sector…”

Section: The Kink-sector Tadpolementioning

confidence: 99%

“…The conventional approach [1,2,3,4] to the computation of the mass of a quantum soliton is as follows. One begins with a Hamiltonian which defines a theory and introduces a one-soliton sector Hamiltonian that describes the same physics in terms of the field expanded about the classical soliton solution.…”

Section: Introductionmentioning

confidence: 99%

Cut-Off Kinks

Evslin¹,

Royston²,

Zhang³

2022

Preprint

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We answer the question: If a vacuum sector Hamiltonian is regularized by an energy cutoff, how is the one-kink sector Hamiltonian regularized? We find that it is not regularized by an energy cutoff, indeed normal modes of all energies are present in the kink Hamiltonian, but rather the decomposition of the field into normal mode operators yields coefficients which lie on a constrained surface that forces them to become small for energies above the cutoff. This explains the old observation that an energy cutoff of the kink Hamiltonian leads to an incorrect one-loop kink mass. To arrive at our conclusion, we impose that the regularized kink sector Hamiltonian is unitarily equivalent to the regularized vacuum sector Hamiltonian. This condition implies that the two regularized Hamiltonians have the same spectrum and so guarantees that the kink Hamiltonian yields the correct kink mass.

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“…[1] to Refs. [20,21]. So far these calculations have been largely at one loop, where they are described by a free theory, with the exception of integrable and supersymmetric models.…”

Section: Remarksmentioning

confidence: 99%

Two-Loop Scalar Kinks

Evslin,

Guo

2020

Preprint

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At one loop, quantum kinks are described by a sum of quantum harmonic oscillator Hamiltonians, and the ground state is just the product of the oscillator ground states. Two-loop kink masses are only known in integrable and supersymmetric cases and two-loop states have never been found. We find the two-loop kink mass and explicitly construct the two-loop kink ground state in a scalar field theory with an arbitrary nonderivative potential. We use a coherent state operator which maps the vacuum sector to the kink sector, allowing all states to be treated with a single Hamiltonian which needs to be renormalized only once, eliminating the need for regulator matching conditions. Our calculation is greatly simplified by a recently introduced alternative to collective coordinates, in which the kink momentum is fixed perturbatively.

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Quantum Corrections to Solitons in the $Φ^8$ Model

Cited by 4 publications

References 17 publications

A reduced inner product for kink states

A reduced inner product for kink states

Cut-Off Kinks

Two-Loop Scalar Kinks

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