Noncommutativity from the symplectic point of view

Abstract

The great deal in noncommutative (NC) field theories started when it was noted that NC spaces naturally arise in string theory with a constant background magnetic field in the presence of $D$-branes. Besides their origin in string theories and branes, NC field theories have been studied extensively in many branches of physics. In this work we explore how NC geometry can be introduced into a commutative field theory besides the usual introduction of the Moyal product. We propose a systematic new way to introduce NC geometry into commutative systems, based mainly on the symplectic approach. Further, as example, this formalism describes precisely how to obtain a Lagrangian description for the NC version of some systems reproducing well known theories.

6 pages, Revtex4. Final version to appear in Int. J. Mod. Phys. A

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Cited by in corpus (9)

• Analysis of constrained theories without use of primary constraints
• Lagrangian formulation for noncommutative nonlinear systems
• Noncommutative cosmological models coupled to a perfect fluid and a cosmological constant
• Noncommutative Mapping from the symplectic formalism
• Hořava-Lifshitz cosmological models in noncommutative space-times
• QCD gauge symmetries through Faddeev-Jackiw symplectic method
• Noncommutativity and Duality through the Symplectic Embedding Formalism
• Noncommutative approach to diagnose degenerate Higgs bosons at 125 GeV
• An alternative way to explain how non-commutativity arises in the bosonic string theory