An Interpretation of Noncommutative Field Theory in Terms of a Quantum Shift

Abstract

Noncommutative coordinates are decomposed into a sum of geometrical ones and a universal quantum shift operator. With the help of this operator, the mapping of a commutative field theory into a noncommutative field theory (NCFT) is introduced. A general measure for the Lorentz-invariance violation in NCFT is also derived.

arXiv comment16 pages

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• Quantum complex scalar fields and noncommutativity
• Reinterpreting deformed Heisenberg algebras
• The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space
• Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Non-anticommutative Supersymmetric Field Theory and Quantum Shift
• Noncommutative Deformation of Spinor Zero Mode and ADHM Construction
• T-Minkowski noncommutative spacetimes I: Poincaré groups, differential calculi and braiding
• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory. II
• ${\pi }^{+}{\pi }^{+}$ and ${\pi }^{+}{\pi }^{-}$ colliding in noncommutative space