U(1) gauge invariant noncommutative Schrödinger theory and gravity

Abstract

We consider the complex, massive Klein-Gordon field living in the noncommutative space, and coupled to noncommutative electromagnetic fields. After employing the Seiberg-Witten map to first order, we analyze the noncommutative Klein-Gordon theory as $c$, the velocity of light, goes to infinity. We show that the theory exhibits a regular "magnetic" limit only for certain forms of magnetic fields. The resulting theory is nothing but the Schrödinger theory in a gravitational background generated by the gauge fields.

15 pages, LaTeX

References in corpus (5)

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• Canonical Noncommutativity Algebra for the Tetrad Field in General Relativity
• Remarks on the Formulation of Quantum Mechanics on Noncommutative Phase Spaces
• Particle Dynamics And Emergent Gravity
• On the Quantization of Length in Noncommutative Spaces
• Novel Ambiguities in the Seiberg-Witten Map and the Emergent Gravity
• On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes