Locality, Causality and Noncommutative Geometry

Abstract

We analyse the causality condition in noncommutative field theory and show that the nonlocality of noncommutative interaction leads to a modification of the light cone to the light wedge. This effect is generic for noncommutative geometry. We also check that the usual form of energy condition is violated and propose that a new form is needed in noncommutative spacetime. On reduction from light cone to light wedge, it looks like the noncommutative dimensions are effectively washed out and suggests a reformulation of noncommutative field theory in terms of lower dimensional degree of freedom. This reduction of dimensions due to noncommutative geometry could play a key role in explaining the holographic property of quantum gravity.

16 pages, LaTeX, 4 figures

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• Noncommutative Field Theory
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• Non-singular Brans-Dicke collapse in deformed phase space
• Noncommutativity from the string perspective: modification of gravity at a mm without mm sized extra dimensions
• Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
• Noncommutative deformations of quantum field theories, locality, and causality
• Failure of microcausality in noncommutative field theories
• Higher-order theories from the minimal length
• Non-local Matching Condition and Scale-invariant Spectrum in Bouncing Cosmology
• Past and future blurring at fundamental length scale
• Nonequilibrium Dynamics in Noncommutative Spacetime