Minimal scales from an extended Hilbert space

Martin Kober, Piero Nicolini

Research output: Contribution to journalArticlepeer-review


We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our commutators do not depend on positions and momenta and we provide an extension of the coordinate coherent state approach to noncommutative geometry. We explore, as a toy model, the corresponding quantum field theory in a (2+1)-dimensional spacetime. Then we investigate the more realistic case of a (3+1)-dimensional spacetime, foliated into noncommutative planes. As a result, we obtain propagators, which are finite in the ultraviolet as well as the infrared regime.

Original languageEnglish (US)
Article number245024
JournalClassical and Quantum Gravity
Issue number24
StatePublished - Dec 21 2010

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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