arXiv subjects

Hengyuan Guo

Publications and source records attributed to Hengyuan Guo.

13 recordsLinked to original sources

arXiv2026

Quantum Lifts of Noninteger Power Law Field Theories

Field theories whose potentials have noninteger power laws $α$ have found many applications, but are often claimed to have no lift to quantum field theory except as effective models. We define quantum lifts by expanding the classical potential in Hermite polynomials and then normal ordering at a mass scale shifted by a parameter $β$. We find that when $α>2$, for sufficiently large $β$, the vacuum state can be perturbatively expanded in usual Fock states. We apply this to the following problem. The $σ=4$ Pöschl-Teller model has a $ϕ^{5/2}$ potential. As the third derivative of the potential diverges in each vacuum, one expects the three point interactions to diverge in the vacuum. The model's kink has three shape modes and the least bound mode extends so far into the vacuum that its probability of being excited by radiation apparently diverges. We show that a deformation $β$ of order the meson mass or larger is sufficient to tame this divergence, although it nonetheless results in an excitation probability which is enhanced by a $β$-dependent fractional power of the inverse coupling.

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arXiv2026

(De-)Exciting the Third Poschl-Teller Kink

There is a series of scalar models possessing reflectionless kinks whose linear perturbations are described by a Pöschl-Teller potential at integer level $σ$. The cases $σ=1$ and $2$ are the well-known Sine-Gordon and $ϕ^4$ double-well models. The $σ=3$ kink has received relatively little attention because it exhibits a $ϕ^{8/3}$ potential, whose third derivative diverges in the vacuum. In old-fashioned perturbation theory this yields a cubic interaction that diverges far from a kink. We nonetheless use this interaction to calculate the amplitudes and probabilities for incoming radiation to excite or de-excite one of the kink's two shape modes. As each shape mode is localized about the kink, the leading order amplitudes are nonetheless finite. This suggests that the $σ=3$ model is not pathological, but rather its mesons are quantum field theoretic extensions of Znojil's bound states.

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arXiv2025

The Domain Wall String's Anti-Stokes Scattering Cross Section

We consider anti-Stokes scattering, in which a perturbative meson scatters off of a domain wall string's shape mode excitation, de-exciting it. Previously the probability of this process was calculated for a perpendicular incident meson striking the center of a localized shape mode. The answer depended on the profiles of the initial wave packets. In this paper we consider an arbitrary incident angle and impact parameter. In addition to the de-excitation probability, we compute the cross section for this process, which as usual is independent of the details of the wave packets. To our knowledge, this is the first time that a cross section has been defined for the scattering of a bulk degree of freedom with a localized excitation in an extended soliton.

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arXiv2024

(Anti-)Stokes Scattering on the Domain Wall String

In a general (2+1)-dimensional scalar model, we consider the scattering of a single quantum of radiation off a domain wall string, which excites or de-excites the wall's internal shape mode. We refer to these two process as Stokes and anti-Stokes scattering. We calculate the probability densities for these processes to first order in quantum field theory, as a function of incoming momenta and angles. We include both the case in which the incident particle is transmitted and also that in which it bounces backward. Our results are given as finite-dimensional integrals of normal modes and elementary functions, and numerical results are presented in the particular case of the $ϕ^4$ double-well model.

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arXiv2024

Constructing A Finite Tension Domain Wall in $ϕ^4_4$

We have recently claimed that the domain wall in the 3+1 dimensional $ϕ^4$ double-well model can be constructed as a squeezed, coherent state and that at one loop it has a finite tension given general, but unspecified, renormalization conditions. In the present note, we justify this claim by showing that the tadpole is finite and the infrared divergences cancel exactly. Also we carefully treat the renormalization of the normal ordering mass scale. Faddeev and Korepin have stressed that ultraviolet divergences cancel in the soliton sector if they cancel in the vacuum sector when the corresponding calculations are identical in the ultraviolet. We therefore renormalize the divergences in the vacuum sector using a Schrodinger picture prescription, which mirrors closely the analogous calculations in the domain wall sector.

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arXiv2024

A Finite Tension for the $ϕ^4_4$ Domain Wall

In 1+1 dimensions, it is well known that the quantum states corresponding to solitons are well described by coherent states. In his 1975 Erice lectures, Coleman observed that this construction does not extend to higher dimensions, as the coherent states have infinite energy density. He challenged the students to construct the quantum states corresponding to solitons in higher dimensions, a problem which remains unsolved today. However, even in 1+1 dimensions, the correct quantum states are actually given by deformations of coherent states. In the 3+1 dimensional $ϕ^4$ double-well model, we show that the leading deformation, which is just a squeeze, already cancels the one-loop divergence in the energy density of the domain wall soliton.

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arXiv2024

A (2+1)-Dimensional Domain Wall at One-Loop

We consider the domain wall in the (2+1)-dimensional $ϕ^4$ double well model, created by extending the $ϕ^4$ kink in an additional infinite direction. Classically, the tension is $m^3/3λ$ where $λ$ is the coupling and $m$ is the meson mass. At order $O(λ^0)$ all ultraviolet divergences can be removed by normal ordering, less trivial divergences arrive only at the next order. This allows us to easily quantize the domain wall, working at order $O(λ^0)$. We calculate the leading quantum correction to its tension as a two-dimensional integral over a function which is determined analytically. This integral is performed numerically, resulting in $-0.0866m^2$. This correction has previously been computed twice in the literature, and the results of these two computations disagreed. Our result agrees with and so confirms that of Jaimunga, Semenoff and Zarembo. We also find, at this order, the excitation spectrum and a general expression for the one-loop tensions of domain walls in other scalar models.

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arXiv2022

Leading Quantum Correction to the $Φ^4$ Kink Form Factor

Recently, Jarah has constructed the kink form factor relevant to the scattering of an ultrarelativistic meson with an arbitrary nonrelativistic scalar kink. However the formula was only applied to the Sine-Gordon model, where the form factor was long ago determined by Weisz using integrability. In this paper, using various known analytic results for the (1+1)-dimensional real scalar $Φ^4$ model and a kink wave packet construction, we analytically calculate the leading quantum correction to the form factor of the $Φ^4$ kink. We discuss its properties in general and also in the ultra-relativistic meson case and provide a numerical check of our results.

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arXiv2021

Removing Tadpoles in a Soliton Sector

It has long been known that perturbative calculations can be performed in a soliton sector of a quantum field theory by using a soliton Hamiltonian, which is constructed from the defining Hamiltonian by shifting the field by the classical soliton solution. It is also known that even if tadpoles are eliminated in the vacuum sector, they remain in the soliton sector. In this note we show, in the case of quantum kinks at two loops, that the soliton sector tadpoles may be removed by adding certain quantum corrections to the classical solution used in this construction. Stated differently, the renormalization condition that the soliton sector tadpoles vanish may be satisfied by renormalizing the soliton solution.

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arXiv2021

Excited Kinks as Quantum States

At one loop, quantum kinks are described by a sum of quantum harmonic oscillator Hamiltonians, and so their spectra are known exactly. We find the first correction beyond one loop to the quantum states corresponding to kinks with an excited bound or unbound normal mode, and also the corresponding two-loop correction to the energy cost of exciting the normal mode. In the case of unbound normal modes, this correction is equal to sum of the corresponding nonrelativistic kinetic energy plus the usual one-loop correction to the mass of the corresponding plane wave in the absence of a kink. We also sketch a diagrammatic method for such calculations.

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arXiv2021

An Alternative to Collective Coordinates

Collective coordinates provide a powerful tool for separating collective and elementary excitations, allowing both to be treated in the full quantum theory. The price is a canonical transformation which leads to a complicated starting point for subsequent calculations. Sometimes the collective behavior of a soliton is simple but nontrivial, and one is interested in the elementary excitations. We show that in this case an alternative prescription suffices, in which the canonical transformation is not necessary. The use of a nonperturbative operator which creates a soliton state allows the theory to be constructed perturbatively in terms of the soliton normal modes. We show how translation invariance may be perturbatively imposed. We apply this to construct the two-loop ground state of an arbitrary scalar kink.

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arXiv2020

Two-Loop Scalar Kinks

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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arXiv2020

Finite Derivation of the One-Loop Sine-Gordon Soliton Mass

Calculations of quantum corrections to soliton masses generally require both the vacuum sector and the soliton sector to be regularized. The finite part of the quantum correction depends on the assumed relation between these regulators when both are taken to infinity. Recently, in the case of quantum kinks, a manifestly finite prescription for the calculation of the quantum corrections has been proposed, which uses the kink creation operator to relate the two sectors. In this note, we test this new prescription by calculating the one-loop correction to the Sine-Gordon soliton mass, reproducing the well-known result which has been derived using integrability.

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