The Casimir effect for nonlinear sigma models and the Mermin-Wagner-Hohenberg-Coleman theorem

Antonino Flachi, Vincenzo Vitagliano

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


The quantum vacuum (Casimir) energy arising from noninteracting massless quanta is known to induce a long-range force, while decays exponentially for massive fields and separations larger than the inverse mass of the quanta involved. Here, we show that the interplay between dimensionality and nonlinearities in the field theory alters this behaviour in a nontrivial way. We argue that the changes are intimately related to the Mermin-Wagner-Hohenberg-Coleman theorem, and illustrate this situation using a nonlinear sigma model as a working example. We compute the quantum vacuum energy, which consists of the usual Casimir contribution plus a semiclassical contribution, and find that the vacuum-induced force is long-ranged at large distance, while displays a complex behaviour at small separations. Finally, even for this relatively simple set-up, we show that nonlinearities are generally responsible for modulations in the force as a function of the coupling constant and the temperature.

Original languageEnglish
Article number265401
JournalJournal of Physics A: Mathematical and Theoretical
Issue number26
Publication statusPublished - 2021 Jul

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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