Momentum gauge fields from curved momentum space through Kaluza-Klein reduction

Eduardo Guendelman, Fabian Wagner

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this work we investigate the relation between curved momentum space and momentum-dependent gauge fields. While the former is a classic idea that has been shown to be tied to minimal-length models, the latter constitutes a relatively recent development in quantum gravity phenomenology. In particular, the gauge principle in momentum space amounts to a modification of the position operator of the form X ˆ μ → X ˆ μ − g A μ ( P ˆ ) akin to a gauge-covariant derivative in momentum space according to the minimal coupling prescription. Here, we derive both effects from a Kaluza-Klein reduction of a higher-dimensional geometry exhibiting curvature in momentum space. The interplay of the emerging gauge fields as well as the remaining curved momentum space lead to modifications of the Heisenberg algebra. While the gauge fields imply Moyal-type noncommutativity dependent on the analogue field strength tensor, the dimensionally reduced curved momentum space geometry translates to a Snyder-type noncommutative geometry.

Original languageEnglish
Article number135007
JournalClassical and Quantum Gravity
Issue number13
StatePublished - 6 Jul 2023


  • Kaluza-Klein reduction
  • momentum gauge fields
  • noncommutative space time

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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