Spatially modulated vacua in a Lorentz-invariant scalar field theory

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


Spatial modulation has been studied for a long time in condensed matter, nuclear matter and quark matter, where the manifest Lorentz invariance is lost due to the finite density/temperature effects and so on. In this paper, spatially modulated vacua at zero temperature and zero density are studied in Lorentz invariant field theories. We first propose an adaptation of the Nambu–Goldstone theorem to higher derivative theories under the assumption of the absence of ghosts: when a global symmetry is spontaneously broken due to vacuum expectation values of space-time derivatives of fields, a Nambu–Goldstone (NG) boson appears without a canonical kinetic (quadratic derivative) term with a quartic derivative term in the modulated direction while a Higgs boson appears with a canonical kinetic term. We demonstrate this in a simple model allowing (meta)stable modulated vacuum of a phase modulation (Fulde–Ferrell state), where an NG mode associated with spontaneously broken translational and U(1) symmetries appears.

Original languageEnglish
Article number754
JournalEuropean Physical Journal C
Issue number9
Publication statusPublished - 2018 Sept 1

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Physics and Astronomy (miscellaneous)


Dive into the research topics of 'Spatially modulated vacua in a Lorentz-invariant scalar field theory'. Together they form a unique fingerprint.

Cite this