Advertisement

Journal of High Energy Physics

, 2019:161 | Cite as

Manifestly finite derivation of the quantum kink mass

  • Jarah EvslinEmail author
Open Access
Regular Article - Theoretical Physics
First Online:
  • 10 Downloads

Abstract

In 1974 Dashen, Hasslacher and Neveu calculated the leading quantum correction to the mass of the kink in the scalar ϕ4 theory in 1+1 dimensions. The derivation relies on the identification of the perturbations about the kink as solutions of the Pöschl-Teller (PT) theory. They regularize the theory by placing it in a periodic box, although the kink is not itself periodic. They also require an ad hoc identification of plane wave and PT states which is difficult to interpret in the decompactified limit. We rederive the mass using the kink operator to recast this problem in terms of the PT Hamiltonian which we explicitly diagonalize using its exact eigenstates. We normal order from the beginning, rendering our theory finite so that no compactification is necessary. In our final expression for the kink mass, the form of the PT potential disappears, suggesting that our mass formula applies to other quantum solitons.

Keywords

Solitons Monopoles and Instantons Field Theories in Lower Dimensions Nonperturbative Effects 
Download to read the full article text

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

References

  1. [1]
    J.-L. Gervais and B. Sakita, Extended Particles in Quantum Field Theories, Phys. Rev.D 11 (1975) 2943 [INSPIRE].ADSGoogle Scholar
  2. [2]
    G. Delfino, W. Selke and A. Squarcini, Vortex mass in the three-dimensional O(2) scalar theory, Phys. Rev. Lett.122 (2019) 050602 [arXiv:1808.09276] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    D. Davies, Quantum Solitons in any Dimension: Derrick’s Theorem v. AQFT, arXiv:1907.10616 [INSPIRE].
  4. [4]
    K. Hepp, The Classical Limit for Quantum Mechanical Correlation Functions, Commun. Math. Phys.35 (1974) 265 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    S. Mandelstam, Soliton Operators for the Quantized sine-Gordon Equation, Phys. Rev.D 11 (1975) 3026 [INSPIRE].ADSMathSciNetGoogle Scholar
  6. [6]
    J.G. Taylor, Solitons as Infinite Constituent Bound States, Annals Phys.115 (1978) 153 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    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 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S. Flügge, Practical Quantum Mechanics, Springer-Verlag (1999).Google Scholar
  9. [9]
    J. Lekner, Reflectionless eigenstates of the sech2potential, Am. J. Phys.75 (2007) 1151.ADSCrossRefGoogle Scholar
  10. [10]
    M. Blasone and P. Jizba, Topological defects as inhomogeneous condensates in quantum field theory: Kinks in (1 + 1)-dimensional λψ 4theory, Annals Phys.295 (2002) 230 [hep-th/0108177] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    G. ’t Hooft, Topology of the Gauge Condition and New Confinement Phases in Nonabelian Gauge Theories, Nucl. Phys.B 190 (1981) 455 [INSPIRE].
  12. [12]
    S. Mandelstam, Vortices and Quark Confinement in Nonabelian Gauge Theories, Phys. Rept.23 (1976) 245 [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys.B 426 (1994) 19 [Erratum ibid.B 430 (1994) 485] [hep-th/9407087] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Institute of Modern PhysicsLanzhouChina
  2. 2.China University of the Chinese Academy of SciencesBeijingChina

Personalised recommendations