Symplectic Quantization of Open Strings and Noncommutativity in Branes

Abstract

We show how to translate boundary conditions into constraints in the symplectic quantization method by an appropriate choice of generalized variables. This way the symplectic quantization of an open string attached to a brane in the presence of an antisymmetric background field reproduces the non commutativity of the brane coordinates.

We included a comparison with previous results obtained from Dirac quantization, emphasizing the fact that in the symplectic case the boundary conditions, that lead to the non commutativity, show up from the direct application of the standard method. Version to appear in Phys. Rev. D

References in corpus (4)

• String Theory and Noncommutative Geometry
• Constrained Quantization of Open String in Background B Field and Noncommutative D-brane
• Dirac Quantization of Open Strings and Noncommutativity in Branes
• Boundary Conditions as Dirac Constraints

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• Symplectic Embedding of a Massive Vector-Tensor Theory with Topological Coupling
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• The Reduced Phase Space of An Open String in The Background B-Field
• Strings in pp-wave background and background B-field from membrane and its symplectic quantization
• Gauge invariant actions for the noncommutative phase-space relativistic particle