Dynamical Noncommutativity and Noether Theorem in Twisted φ^{⋆ 4} Theory

2008/03/31 by Paolo Aschieri, Leonardo Castellani, Marija Dimitrijević Ćirić +1 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th

paper · pdf · doi:10.1007/s11005-008-0247-6

published as Lett.Math.Phys.85:39-53,2008 · 15 pages LaTeX, minor typos, added references

openalex publication_date 2008/06/23 · arxiv created 2008/07/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29

Abstract

A ⋆-product is defined via a set of commuting vector fields X_a = e_a^μ(x) ∂_μ, and used in a phi^*4 theory coupled to the e_a^μ(x) fields. The ⋆-product is dynamical, and the vacuum solution phi =0, e_a^μ(x)=delta_a^μreproduces the usual Moyal product. The action is invariant under rigid translations and Lorentz rotations, and the conserved energy-momentum and angular momentum tensors are explicitly derived.

Citations

• The energy-momentum tensor on noncommutative spaces - some pedagogical comments
• On the principles of elementary quantum mechanics
• Quantenmechanik und Gruppentheorie
• Position-dependent noncommutative products: Classical construction and field theory
• A gravity theory on noncommutative spaces
• Quantum mechanics as a statistical theory
• An Introduction to Noncommutative Spaces and their Geometry

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