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arxiv: 2605.22285 · v2 · pith:RWYLW4YAnew · submitted 2026-05-21 · ✦ hep-th

Krakow Lectures on Scalar Quantum Solitons

Jarah Evslin This is my paper

Pith reviewed 2026-06-30 16:29 UTC · model grok-4.3

classification ✦ hep-th
keywords quantum solitonsLinearized Soliton Perturbation Theorysqueezed coherent statesperturbative correctionskink-meson scatteringdomain wall solitonsHamiltonian approach
0
0 comments X

The pith

Linearized Soliton Perturbation Theory constructs quantum soliton states explicitly as squeezed coherent states plus perturbative corrections.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Linearized Soliton Perturbation Theory as a Hamiltonian approach focused on building quantum soliton states directly. These states are formed as squeezed coherent states with added perturbative corrections, which supports systematic computation of multi-loop corrections to both the states and their masses. An inner product is defined for non-normalizable momentum eigenstates and used to handle kink-meson scattering. The method is also applied to domain wall solitons. A reader would care because it supplies concrete tools for quantum corrections in systems where solitons appear.

Core claim

Linearized Soliton Perturbation Theory is a Hamiltonian approach that explicitly constructs the soliton states as squeezed coherent states plus perturbative corrections. It computes multi-loop corrections to states and masses. An inner product suitable for non-normalizable momentum eigenstates is introduced and applied to kink-meson scattering, while domain wall solitons are also discussed.

What carries the argument

Linearized Soliton Perturbation Theory (LSPT), which constructs soliton states explicitly in a Hamiltonian framework as squeezed coherent states plus perturbative corrections.

If this is right

  • Multi-loop corrections to soliton states and masses can be calculated order by order.
  • Kink-meson scattering amplitudes become accessible through the defined inner product for non-normalizable states.
  • The construction applies equally to domain wall solitons.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The squeezed coherent state form may extend naturally to soliton calculations in models with additional fields or interactions.
  • The inner product for non-normalizable states could be adapted to other momentum eigenstates in quantum field theory.
  • Numerical lattice simulations of soliton dynamics might provide an independent test of the perturbative state corrections.

Load-bearing premise

Quantum soliton states admit an explicit construction as squeezed coherent states plus perturbative corrections within a Hamiltonian framework.

What would settle it

A direct check that the constructed states fail to satisfy the time-independent Schrödinger equation at the claimed perturbative order, or that the inner product yields inconsistent scattering amplitudes for kink-meson processes.

Figures

Figures reproduced from arXiv: 2605.22285 by Jarah Evslin.

Figure 1
Figure 1. Figure 1: The first three terms in Q2 can be represented abstractly as two-loop diagrams. Each factor of I(x) corresponds to a loop at the vertex x while each gk(x) is an internal line corresponding to a meson with momentum k or a shape mode. The three terms on the first line have simple diagrammatic interpretations, shown in [PITH_FULL_IMAGE:figures/full_fig_p055_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The last three terms in Q2 can be represented abstractly as two-loop diagrams involving zero modes, which are depicted as dashed lines. Here the same procedure does not apply as we do not have an equation satisfied by V (n−1)( √ λf(x))g. Also, we do not obtain another Vk1···kn interaction as, after integration by parts, will have some g ′ . Our strategy will be to separate out the g ′ factors using the com… view at source ↗
read the original abstract

We give a pedagogical introduction to Linearized Soliton Perturbation Theory (LSPT), a new and efficient tool for calculations involving quantum solitons. It is a Hamiltonian approach with a focus on explicitly constructing the soliton states. These states are squeezed, coherent states plus perturbative corrections. We will describe multi-loop corrections to states and their masses. An inner product suitable for non-normalizable momentum eigenstates will be introduced and applied to kink-meson scattering. We will also discuss domain wall solitons.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript provides a pedagogical introduction to Linearized Soliton Perturbation Theory (LSPT), presented as a Hamiltonian framework for explicitly constructing quantum soliton states. These states are described as squeezed coherent states supplemented by perturbative corrections, with extensions to multi-loop corrections for both states and masses. An inner product is introduced to handle non-normalizable momentum eigenstates and is applied to kink-meson scattering; domain wall solitons are also discussed.

Significance. If the explicit constructions and inner-product definition are valid and reproducible, LSPT could offer a practical computational tool for soliton-related observables in scalar QFT, particularly by making state constructions and scattering amplitudes more direct within a Hamiltonian setting. The pedagogical framing and focus on explicit constructions are strengths that could aid adoption if the derivations are self-contained.

minor comments (2)
  1. [Introduction] The abstract refers to 'multi-loop corrections to states and their masses' and an 'inner product suitable for non-normalizable momentum eigenstates' without indicating the section or equation where the explicit form of the inner product or the loop expansion is derived; adding a roadmap in the introduction would improve readability.
  2. The claim that LSPT is 'new and efficient' would benefit from a brief comparison (even qualitative) to existing methods such as collective-coordinate quantization or semiclassical expansions, to clarify the incremental advance.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their summary of our manuscript and for noting the potential of LSPT as a practical Hamiltonian tool for soliton observables. The pedagogical focus on explicit state constructions is intentional, and we are pleased this was recognized. No specific major comments were provided in the report, so we have no point-by-point responses at this time. We remain available to address any further questions or to expand on the derivations if the referee wishes to examine particular sections in more detail.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained construction

full rationale

The paper presents LSPT as an explicit Hamiltonian construction of soliton states (squeezed coherent states plus perturbative corrections), multi-loop corrections, and an inner product for momentum eigenstates, applied to kink-meson scattering. No load-bearing step reduces by the paper's own equations or self-citation to a fitted input, self-definition, or renamed known result. The abstract and description frame the work as a new pedagogical tool rather than a redefinition of quantities. Absent any quoted derivation chain that equates output to input by construction, the central claims retain independent content. This matches the expected honest non-finding for a construction-focused manuscript.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no free parameters, axioms, or invented entities are specified.

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Works this paper leans on

87 extracted references · 84 canonical work pages · 17 internal anchors

  1. [1]

    Defect states in polyacetylene and polydiacetylene,

    A. R. Bishop, “Defect states in polyacetylene and polydiacetylene,” Solid State Com- mun. 33 (1980), 955 doi:10.1016/0038-1098(80)90289-6

    work page doi:10.1016/0038-1098(80)90289-6 1980

  2. [2]

    A Nonlinear theory of strong interactions,

    T. H. R. Skyrme, “A Nonlinear theory of strong interactions,” Proc. Roy. Soc. Lond. A 247 (1958), 260-278 doi:10.1098/rspa.1958.0183

    work page doi:10.1098/rspa.1958.0183 1958

  3. [3]

    Examples for BPS solitons destabilized by quantum ef- fects,

    W. J. Meyer and H. Weigel, “Examples for BPS solitons destabilized by quantum ef- fects,” [arXiv:2506.05006 [hep-th]]

    work page arXiv

  4. [4]

    Vortex mass in the three-dimensional $O(2)$ scalar theory

    G. Delfino, W. Selke and A. Squarcini, “Vortex mass in the three- dimensional O(2) scalar theory,” Phys. Rev. Lett. 122 (2019) no.5, 050602 doi:10.1103/PhysRevLett.122.050602 [arXiv:1808.09276 [cond-mat.stat-mech]]. 95

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.122.050602 2019

  5. [5]

    Quantum Solitons in any Dimension: Derrick’s Theorem v. AQFT,

    D. Davies, “Quantum Solitons in any Dimension: Derrick’s Theorem v. AQFT,” [arXiv:1907.10616 [hep-th]]

    work page arXiv 1907

  6. [6]

    One-loop kink mass shifts: a computational approach

    A. Alonso-Izquierdo and J. Mateos Guilarte, “One-loop kink mass shifts: A Computational approach,” Nucl. Phys. B 852 (2011), 696-735 doi:10.1016/j.nuclphysb.2011.07.005 [arXiv:1107.2216 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.nuclphysb.2011.07.005 2011

  7. [7]

    Quantum corrections to soliton energies,

    N. Graham and H. Weigel, “Quantum corrections to soliton energies,” Int. J. Mod. Phys. A 37 (2022) no.19, 2241004 doi:10.1142/S0217751X22410044 [arXiv:2201.12131 [hep-th]]

    work page doi:10.1142/s0217751x22410044 2022

  8. [8]

    A Classical-Quantum Correspondence and Backreaction

    T. Vachaspati and G. Zahariade, “Classical-quantum correspondence and backre- action,” Phys. Rev. D 98 (2018) no.6, 065002 doi:10.1103/PhysRevD.98.065002 [arXiv:1806.05196 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.98.065002 2018

  9. [9]

    Classical-Quantum Correspondence for Fields,

    T. Vachaspati and G. Zahariade, “Classical-Quantum Correspondence for Fields,” JCAP 09 (2019), 015 doi:10.1088/1475-7516/2019/09/015 [arXiv:1807.10282 [hep-th]]

    work page doi:10.1088/1475-7516/2019/09/015 2019

  10. [10]

    Extended Particles in Quantum Field Theories,

    J. L. Gervais and B. Sakita, “Extended Particles in Quantum Field Theories,” Phys. Rev. D 11 (1975), 2943 doi:10.1103/PhysRevD.11.2943

    work page doi:10.1103/physrevd.11.2943 1975

  11. [11]

    Quantum Expansion of Soliton Solutions,

    N. H. Christ and T. D. Lee, “Quantum Expansion of Soliton Solutions,” Phys. Rev. D 12 (1975), 1606 doi:10.1103/PhysRevD.12.1606

    work page doi:10.1103/physrevd.12.1606 1975

  12. [12]

    Canonical Quantization of Nonlinear Waves,

    E. Tomboulis, “Canonical Quantization of Nonlinear Waves,” Phys. Rev. D 12 (1975), 1678 doi:10.1103/PhysRevD.12.1678

    work page doi:10.1103/physrevd.12.1678 1975

  13. [13]

    Point Canonical Transformations in Path Integral,

    J. L. Gervais and A. Jevicki, “Point Canonical Transformations in Path Integral,” Nucl. Phys. B 110 (1976), 93-112 doi:10.1016/0550-3213(76)90422-3

    work page doi:10.1016/0550-3213(76)90422-3 1976

  14. [14]

    Collective co- ordinate fix in the path integral,

    A. Bhattacharya, J. Cotler, A. Dersy and M. D. Schwartz, “Collective co- ordinate fix in the path integral,” Phys. Rev. D 110 (2024) no.11, 116023 doi:10.1103/PhysRevD.110.116023 [arXiv:2402.18633 [hep-th]]

    work page doi:10.1103/physrevd.110.116023 2024

  15. [15]

    False vacuum decay of excited states in finite-time in- stanton calculus,

    B. Garbrecht and N. Wagner, “False vacuum decay of excited states in finite-time in- stanton calculus,” [arXiv:2412.20431 [hep-th]]

    work page arXiv

  16. [16]

    Gravitational form factors of a kink in 1 + 1 dimensional ϕ4 model,

    H. Ito and M. Kitazawa, “Gravitational form factors of a kink in 1 + 1 dimensional ϕ4 model,” JHEP 08 (2023), 033 doi:10.1007/JHEP08(2023)033 [arXiv:2302.08762 [hep- th]]. 96

    work page doi:10.1007/jhep08(2023)033 2023

  17. [17]

    Framework for the Forced Soliton Equation: Regularization, Numerical Solutions, and Perturbation Theory,

    Z. J. Allamon, Q. A. Hales, A. B. Royston, D. L. Rutledge and E. A. Yozie, “Framework for the Forced Soliton Equation: Regularization, Numerical Solutions, and Perturbation Theory,” [arXiv:2412.09487 [hep-th]]

    work page arXiv

  18. [18]

    Manifestly Finite Derivation of the Quantum Kink Mass,

    J. Evslin, “Manifestly Finite Derivation of the Quantum Kink Mass,” JHEP 11 (2019), 161 doi:10.1007/JHEP11(2019)161 [arXiv:1908.06710 [hep-th]]

    work page doi:10.1007/jhep11(2019)161 2019

  19. [19]

    Two-Loop Scalar Kinks,

    J. Evslin and H. Guo, “Two-Loop Scalar Kinks,” Phys. Rev. D 103 (2021) no.12, 125011 doi:10.1103/PhysRevD.103.125011 [arXiv:2012.04912 [hep-th]]

    work page doi:10.1103/physrevd.103.125011 2021

  20. [20]

    Horologium Oscillatorium, Sive De Motu Pendulorum Ad Horologia Ap- tato Demonstrationes Geometricae

    C. Huygens, “Horologium Oscillatorium, Sive De Motu Pendulorum Ad Horologia Ap- tato Demonstrationes Geometricae. ” Latin. Paris: F. Muguet, (1673)

  21. [21]

    A quantum-theoretical reinterpretation of kinematic and mechanical relations,

    W. Heisenberg, “A quantum-theoretical reinterpretation of kinematic and mechanical relations,” Z. Phys. 33 (1925), 879-893 doi:10.1007/BF01328377

    work page doi:10.1007/bf01328377 1925

  22. [22]

    Finkelstein, “KINKS,” J

    D. Finkelstein, “KINKS,” J. Math. Phys. 7 (1966), 1218-1225 doi:10.1063/1.1705025

    work page doi:10.1063/1.1705025 1966

  23. [23]

    Quantum Instabilities of Solitons

    H. Weigel, “Quantum Instabilities of Solitons,” AIP Conf. Proc. 2116 (2019) no.1, 170002 doi:10.1063/1.5114153 [arXiv:1907.10942 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1063/1.5114153 2019

  24. [24]

    Analytical Descriptions of Ultrashort Optical Pulse Propagation in a Res- onant Medium,

    G. l. Lamb, “Analytical Descriptions of Ultrashort Optical Pulse Propagation in a Res- onant Medium,” Rev. Mod. Phys. 43 (1971), 99-124 doi:10.1103/RevModPhys.43.99

    work page doi:10.1103/revmodphys.43.99 1971

  25. [25]

    Exact Solution of the Sine-Gordon Equation for Multiple Collisions of Soli- tons,

    R. Hirota, “Exact Solution of the Sine-Gordon Equation for Multiple Collisions of Soli- tons,” Jour. Phys. Soc. Japan. 33 (1972), 1459-1463 doi:10.1143/JPSJ.33.1459

    work page doi:10.1143/jpsj.33.1459 1972

  26. [26]

    No saturation of the quantum Bogomolnyi bound by two-dimensional supersymmetric solitons

    A. Rebhan and P. van Nieuwenhuizen, “No saturation of the quantum Bogomolnyi bound by two-dimensional supersymmetric solitons,” Nucl. Phys. B 508 (1997), 449- 467 doi:10.1016/S0550-3213(97)00625-1 [arXiv:hep-th/9707163 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/s0550-3213(97)00625-1 1997

  27. [27]

    Classical Lumps and their Quantum Descendents,

    S. R. Coleman, “Classical Lumps and their Quantum Descendents,” Subnucl. Ser. 13 (1977), 297 PRINT-77-0088 (HAR V ARD)

    1977

  28. [28]

    Effective mass and correlation length of nucleon constituents,

    P. Vinciarelli, “Effective mass and correlation length of nucleon constituents,” Lett. Nuovo Cim. 4S2 (1972), 905-909 doi:10.1007/BF02756261

    work page doi:10.1007/bf02756261 1972

  29. [29]

    Effective Action for Composite Opera- tors,

    J. M. Cornwall, R. Jackiw and E. Tomboulis, “Effective Action for Composite Opera- tors,” Phys. Rev. D 10 (1974), 2428-2445 doi:10.1103/PhysRevD.10.2428

    work page doi:10.1103/physrevd.10.2428 1974

  30. [30]

    Mass Formulas for Static Solitons,

    K. E. Cahill, A. Comtet and R. J. Glauber, “Mass Formulas for Static Solitons,” Phys. Lett. B 64 (1976), 283-285 doi:10.1016/0370-2693(76)90202-1 97

    work page doi:10.1016/0370-2693(76)90202-1 1976

  31. [31]

    Nonperturbative Methods and Extended Hadron Models in Field Theory 2. Two-Dimensional Models and Extended Hadrons,

    R. F. Dashen, B. Hasslacher and A. Neveu, “Nonperturbative Methods and Extended Hadron Models in Field Theory 2. Two-Dimensional Models and Extended Hadrons,” Phys. Rev. D 10 (1974) 4130. doi:10.1103/PhysRevD.10.4130

    work page doi:10.1103/physrevd.10.4130 1974

  32. [32]

    Normal ordering normal modes,

    J. Evslin, “Normal ordering normal modes,” Eur. Phys. J. C 81 (2021) no.1, 92 doi:10.1140/epjc/s10052-021-08890-7 [arXiv:2007.05741 [hep-th]]

    work page doi:10.1140/epjc/s10052-021-08890-7 2021

  33. [33]

    A Resonance in Elastic Kink-Meson Scattering,

    B. Bayarsaikhan and J. Evslin, “A Resonance in Elastic Kink-Meson Scattering,” [arXiv:2603.26070 [hep-th]]

    work page arXiv

  34. [34]

    Spectral Walls in Soliton Collisions

    C. Adam, K. Oles, T. Romanczukiewicz and A. Wereszczynski, “Spectral Walls in Soliton Collisions,” Phys. Rev. Lett. 122 (2019) no.24, 241601 doi:10.1103/PhysRevLett.122.241601 [arXiv:1903.12100 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.122.241601 2019

  35. [35]

    Spectral walls at one loop,

    J. Evslin, C. Halcrow, T. Romanczukiewicz and A. Wereszczynski, “Spectral walls at one loop,” Phys. Rev. D 105 (2022) no.12, 125002 doi:10.1103/PhysRevD.105.125002 [arXiv:2202.08249 [hep-th]]

    work page doi:10.1103/physrevd.105.125002 2022

  36. [36]

    Kink form factors,

    J. Evslin, “Kink form factors,” JHEP 07 (2022), 033 doi:10.1007/JHEP07(2022)033 [arXiv:2203.15445 [hep-th]]

    work page doi:10.1007/jhep07(2022)033 2022

  37. [37]

    Leading quantum correction to the Φ4 kink form factor,

    H. Guo, “Leading quantum correction to the Φ4 kink form factor,” Phys. Rev. D 106 (2022) no.9, 096001 doi:10.1103/PhysRevD.106.096001 [arXiv:2209.03650 [hep-th]]

    work page doi:10.1103/physrevd.106.096001 2022

  38. [38]

    A reduced inner product for kink states,

    J. Evslin and H. Liu, “A reduced inner product for kink states,” JHEP 03 (2023), 070 doi:10.1007/JHEP03(2023)070 [arXiv:2212.10344 [hep-th]]

    work page doi:10.1007/jhep03(2023)070 2023

  39. [39]

    The two-loop ϕ4 kink mass,

    J. Evslin, “The two-loop ϕ4 kink mass,” Phys. Lett. B 822 (2021), 136628 doi:10.1016/j.physletb.2021.136628 [arXiv:2109.05852 [hep-th]]

    work page doi:10.1016/j.physletb.2021.136628 2021

  40. [40]

    Reflection coefficient of a reflectionless kink,

    J. Evslin and H. Liu, “Reflection coefficient of a reflectionless kink,” Phys. Rev. D 109 (2024) no.8, 085019 doi:10.1103/PhysRevD.109.085019 [arXiv:2402.17968 [hep-th]]

    work page doi:10.1103/physrevd.109.085019 2024

  41. [41]

    Evidence for the unbinding of the ϕ4 kink’s shape mode,

    J. Evslin, “Evidence for the unbinding of the ϕ4 kink’s shape mode,” JHEP 09 (2021), 009 doi:10.1007/JHEP09(2021)009 [arXiv:2104.14387 [hep-th]]

    work page doi:10.1007/jhep09(2021)009 2021

  42. [42]

    On the formulation of quantized field theories,

    H. Lehmann, K. Symanzik and W. Zimmermann, “On the formulation of quantized field theories,” Nuovo Cim. 1 (1955), 205-225 doi:10.1007/BF02731765

    work page doi:10.1007/bf02731765 1955

  43. [43]

    Elastic Kink-Meson scattering,

    J. Evslin and H. Liu, “Elastic Kink-Meson scattering,” JHEP 04 (2024), 072 doi:10.1007/JHEP04(2024)072 [arXiv:2311.14369 [hep-th]]. 98

    work page doi:10.1007/jhep04(2024)072 2024

  44. [44]

    Meson production from kink-meson scattering,

    H. Liu, J. Evslin and B. Zhang, “Meson production from kink-meson scattering,” Phys. Rev. D 107 (2023) no.2, 025012 doi:10.1103/PhysRevD.107.025012 [arXiv:2211.01794 [hep-th]]

    work page doi:10.1103/physrevd.107.025012 2023

  45. [45]

    Comments on nonlinear wave equations as models for elementary par- ticles,

    G. H. Derrick, “Comments on nonlinear wave equations as models for elementary par- ticles,” J. Math. Phys. 5 (1964), 1252-1254 doi:10.1063/1.1704233

    work page doi:10.1063/1.1704233 1964

  46. [46]

    Internal Symmetry and the Semiclassical Method in Quantum Field Theory,

    R. Rajaraman and E. J. Weinberg, “Internal Symmetry and the Semiclassical Method in Quantum Field Theory,” Phys. Rev. D 11 (1975), 2950 doi:10.1103/PhysRevD.11.2950

    work page doi:10.1103/physrevd.11.2950 1975

  47. [47]

    On Solitons with an Abelian Charge in Scalar Field Theories. 1. Clas- sical Theory and Bohr-Sommerfeld Quantization,

    C. Montonen, “On Solitons with an Abelian Charge in Scalar Field Theories. 1. Clas- sical Theory and Bohr-Sommerfeld Quantization,” Nucl. Phys. B 112 (1976), 349-357 doi:10.1016/0550-3213(76)90537-X

    work page doi:10.1016/0550-3213(76)90537-x 1976

  48. [48]

    Solitary Wave Solution for a Complex One- Dimensional Field,

    S. Sarker, S. E. Trullinger and A. R. Bishop, “Solitary Wave Solution for a Complex One- Dimensional Field,” Phys. Lett. A 59 (1976), 255-258 doi:10.1016/0375-9601(76)90784-2

    work page doi:10.1016/0375-9601(76)90784-2 1976

  49. [49]

    Kink dynamics in the MSTB Model

    A. Alonso-Izquierdo, “Kink dynamics in the MSTB model,” Phys. Scripta 94 (2019) no.8, 085302 doi:10.1088/1402-4896/ab1184 [arXiv:1804.05605 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1402-4896/ab1184 2019

  50. [50]

    Instanton corrections to the MSTB Kink mass,

    J. Evslin, A. García Martín-Caro and A. Wereszczyński, “Instanton corrections to the MSTB Kink mass,” JHEP 04 (2025), 173 doi:10.1007/JHEP04(2025)173 [arXiv:2501.08034 [hep-th]]

    work page doi:10.1007/jhep04(2025)173 2025

  51. [51]

    Degenerate kinks and kink-instantons in two-dimensional scalar field models with N=1 and N=2 supersymmetry,

    E. Ievlev and M. Shifman, “Degenerate kinks and kink-instantons in two-dimensional scalar field models with N=1 and N=2 supersymmetry,” Phys. Rev. D 112 (2025) no.12, 125001 doi:10.1103/8htl-6ncq [arXiv:2509.14324 [hep-th]]

    work page doi:10.1103/8htl-6ncq 2025

  52. [52]

    A (2+1)-dimensional domain wall at one-loop,

    K. Ogundipe, J. Evslin, B. Zhang and H. Guo, “A (2+1)-dimensional domain wall at one-loop,” JHEP 05 (2024), 098 doi:10.1007/JHEP05(2024)098 [arXiv:2403.14062 [hep-th]]

    work page doi:10.1007/jhep05(2024)098 2024

  53. [53]

    An extended Soliton’s zero modes,

    J. Evslin and H. Liu, “An extended Soliton’s zero modes,” JHEP 12 (2025), 015 doi:10.1007/JHEP12(2025)015 [arXiv:2507.18922 [hep-th]]

    work page doi:10.1007/jhep12(2025)015 2025

  54. [54]

    There are no Goldstone bosons in two-dimensions,

    S. R. Coleman, “There are no Goldstone bosons in two-dimensions,” Commun. Math. Phys. 31 (1973), 259-264 doi:10.1007/BF01646487

    work page doi:10.1007/bf01646487 1973

  55. [55]

    On Quantum interacting embedded geometrical objects of various dimen- sions,

    O. Evnin, “On Quantum interacting embedded geometrical objects of various dimen- sions,” UMI-32-36223. 99

  56. [56]

    Local recoil of extended solitons: A String theory example,

    B. Craps, O. Evnin and S. Nakamura, “Local recoil of extended solitons: A String theory example,” JHEP 01 (2007), 050 doi:10.1088/1126-6708/2007/01/050 [arXiv:hep- th/0608123 [hep-th]]

    work page doi:10.1088/1126-6708/2007/01/050 2007

  57. [57]

    Amplitude of the surface tension near the critical point,

    E. Brezin and S. Feng, “Amplitude of the surface tension near the critical point,” Phys. Rev. B 29 (1984), 472-475 doi:10.1103/PhysRevB.29.472

    work page doi:10.1103/physrevb.29.472 1984

  58. [58]

    Tunneling Amplitude and Surface Tension in ϕ4 Theory,

    G. Munster, “Tunneling Amplitude and Surface Tension in ϕ4 Theory,” Nucl. Phys. B 324 (1989), 630-642 doi:10.1016/0550-3213(89)90524-5

    work page doi:10.1016/0550-3213(89)90524-5 1989

  59. [59]

    One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization

    A. Rebhan, P. van Nieuwenhuizen and R. Wimmer, “One loop surface tensions of (su- persymmetric) kink domain walls from dimensional regularization,” New J. Phys. 4 (2002), 31 doi:10.1088/1367-2630/4/1/331 [arXiv:hep-th/0203137 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1367-2630/4/1/331 2002

  60. [60]

    Domain Walls at Finite Temperature,

    C. Aragao de Carvalho, G. C. Marques, A. J. da Silva and I. Ventura, “Domain Walls at Finite Temperature,” Nucl. Phys. B 265 (1986), 45-64 doi:10.1016/0550-3213(86)90406- 2

    work page doi:10.1016/0550-3213(86)90406- 1986

  61. [61]

    Thermal and Quantum Fluctuations around Domain Walls

    C. A. A. de Carvalho, “Thermal and quantum fluctuations around domain walls,” Phys. Rev. D 65 (2002), 065021 [erratum: Phys. Rev. D 66 (2002), 049901] doi:10.1103/PhysRevD.65.065021 [arXiv:hep-ph/0110103 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.65.065021 2002

  62. [62]

    The domain wall soliton’s tension,

    J. Evslin, H. Liu and B. Zhang, “The domain wall soliton’s tension,” Eur. Phys. J. C 85 (2025) no.6, 639 doi:10.1140/epjc/s10052-025-14383-8 [arXiv:2412.20814 [hep-th]]

    work page doi:10.1140/epjc/s10052-025-14383-8 2025

  63. [63]

    Quantum contribution to domain wall tension from spectral methods,

    N. Graham and H. Weigel, “Quantum contribution to domain wall tension from spectral methods,” [arXiv:2505.00119 [hep-th]]

    work page arXiv

  64. [64]

    Scheme Dependence of the One-Loop Domain Wall Tension

    J. Evslin and H. Liu, “Scheme Dependence of the One-Loop Domain Wall Tension,” [arXiv:2505.21856 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv

  65. [65]

    The Particle Spectrum in Model Field Theories from Semiclassical Functional Integral Techniques,

    R. F. Dashen, B. Hasslacher and A. Neveu, “The Particle Spectrum in Model Field Theories from Semiclassical Functional Integral Techniques,” Phys. Rev. D 11 (1975), 3424 doi:10.1103/PhysRevD.11.3424

    work page doi:10.1103/physrevd.11.3424 1975

  66. [66]

    Perturbative approach to time-dependent quantum soli- tons,

    K. Ogundipe and J. Evslin, “Perturbative approach to time-dependent quantum soli- tons,” JHEP 06 (2024), 174 doi:10.1007/JHEP06(2024)174 [arXiv:2403.13232 [hep-th]]

    work page doi:10.1007/jhep06(2024)174 2024

  67. [67]

    Quantum Radiation of Oscillons

    M. P. Hertzberg, “Quantum Radiation of Oscillons,” Phys. Rev. D 82 (2010), 045022 doi:10.1103/PhysRevD.82.045022 [arXiv:1003.3459 [hep-th]]. 100

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.82.045022 2010

  68. [68]

    Quantum Evaporation of Classical Breathers,

    J. Ollé, O. Pujolas, T. Vachaspati and G. Zahariade, “Quantum Evaporation of Classical Breathers,” Phys. Rev. D 100 (2019) no.4, 045011 doi:10.1103/PhysRevD.100.045011 [arXiv:1904.12962 [hep-th]]

    work page doi:10.1103/physrevd.100.045011 2019

  69. [69]

    Perturbative construction of coher- ent states,

    L. Berezhiani, G. Cintia and M. Zantedeschi, “Perturbative construction of coher- ent states,” Phys. Rev. D 109 (2024) no.8, 085018 doi:10.1103/PhysRevD.109.085018 [arXiv:2311.18650 [hep-th]]

    work page doi:10.1103/physrevd.109.085018 2024

  70. [70]

    Quantum Theory of Solitons: Preliminary Version,

    L. D. Faddeev and V. E. Korepin, “Quantum Theory of Solitons: Preliminary Version,” Phys. Rept. 42 (1978), 1-87 doi:10.1016/0370-1573(78)90058-3

    work page doi:10.1016/0370-1573(78)90058-3 1978

  71. [71]

    Quantum corrections to solitons and BPS saturation

    A. Rebhan, P. van Nieuwenhuizen and R. Wimmer, “Quantum corrections to solitons and BPS saturation,” doi:10.1142/9789814277839_0005 [arXiv:0902.1904 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/9789814277839_0005 1904

  72. [72]

    Once more on the BPS bound for the susy kink

    A. Litvintsev and P. van Nieuwenhuizen, “Once more on the BPS bound for the SUSY kink,” [arXiv:hep-th/0010051 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv

  73. [73]

    Fermionic bound states in distinct kinklike backgrounds

    D. Bazeia and A. Mohammadi, “Fermionic bound states in distinct kinklike back- grounds,” Eur. Phys. J. C 77 (2017) no.4, 203 doi:10.1140/epjc/s10052-017-4778-9 [arXiv:1702.00891 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-017-4778-9 2017

  74. [74]

    Fermions on kinks revisited,

    V. Klimashonok, I. Perapechka and Y. Shnir, “Fermions on kinks revisited,” Phys. Rev. D 100 (2019) no.10, 105003 doi:10.1103/PhysRevD.100.105003 [arXiv:1909.12736 [hep-th]]

    work page doi:10.1103/physrevd.100.105003 2019

  75. [75]

    Remarks on sine-Gordon kink– fermion system: localized modes and scattering,

    V. A. Gani, A. Gorina, I. Perapechka and Y. Shnir, “Remarks on sine-Gordon kink– fermion system: localized modes and scattering,” Eur. Phys. J. C 82 (2022) no.8, 757 doi:10.1140/epjc/s10052-022-10707-0 [arXiv:2205.13437 [hep-th]]

    work page doi:10.1140/epjc/s10052-022-10707-0 2022

  76. [76]

    Fermionic spectral walls in kink collisions,

    J. G. F. Campos, A. Mohammadi, J. M. Queiruga, A. Wereszczynski and W. J. Za- krzewski, “Fermionic spectral walls in kink collisions,” JHEP 01 (2023), 071 doi:10.1007/JHEP01(2023)071 [arXiv:2211.07754 [hep-th]]

    work page doi:10.1007/jhep01(2023)071 2023

  77. [77]

    Anomaly and quantum corrections to solitons in two-dimensional theories with minimal supersymmetry

    M. A. Shifman, A. I. Vainshtein and M. B. Voloshin, “Anomaly and quantum corrections to solitons in two-dimensional theories with minimal supersymmetry,” Phys. Rev. D 59 (1999), 045016 doi:10.1103/PhysRevD.59.045016 [arXiv:hep-th/9810068 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.59.045016 1999

  78. [78]

    Topological boundary conditions, the BPS bound, and elimination of ambiguities in the quantum mass of solitons

    H. Nastase, M. A. Stephanov, P. van Nieuwenhuizen and A. Rebhan, “Topological boundary conditions, the BPS bound, and elimination of ambiguities in the quantum mass of solitons,” Nucl. Phys. B 542 (1999), 471-514 doi:10.1016/S0550-3213(98)00773- 1 [arXiv:hep-th/9802074 [hep-th]]. 101

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/s0550-3213(98)00773- 1999

  79. [79]

    Self-gravitating kinks in two-dimensional pseudo-Riemannian universes,

    A. Alonso Izquierdo, W. García Fuertes and J. Mateos Guilarte, “Self-gravitating kinks in two-dimensional pseudo-Riemannian universes,” Phys. Rev. D 101 (2020) no.3, 036020 doi:10.1103/PhysRevD.101.036020 [arXiv:1911.08167 [hep-th]]

    work page doi:10.1103/physrevd.101.036020 2020

  80. [80]

    Revisit on two-dimensional self-gravitating kinks: superpotential for- malism and linear stability,

    Y. Zhong, “Revisit on two-dimensional self-gravitating kinks: superpotential for- malism and linear stability,” JHEP 04 (2021), 118 doi:10.1007/JHEP04(2021)118 [arXiv:2101.10928 [hep-th]]

    work page doi:10.1007/jhep04(2021)118 2021

Showing first 80 references.