Publication: Quantization of the open string on plane-wave limits of dS(n) x S-n and non-commutativity outside branes
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2008-08-11
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Elsevier Science Bv
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The open string on the plane-wave limit of dSn × Sn with constant B2 and dilaton background fields is canonically quantized. This entails solving the classical equations of motion for the string, computing the symplectic form, and defining from its inverse the canonical commutation relations. Canonical quantization is proved to be perfectly suited for this task, since the symplectic form is unambiguously defined and non-singular. The string position and the string momentum operators are shown to satisfy equal-time canonical commutation relations. Noticeably the string position operators define non-commutative spaces for all values of the string world-sheet parameter σ, thus extending non-commutativity outside the branes on which the string endpoints may be assumed to move. The Minkowski space–time limit is smooth and reproduces the results in the literature, in particular non-commutativity gets confined to the endpoints.
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© 2008 Elsevier B.V. All rights reserved.
The authors are grateful to MEC and CAM, Spain for partial support through grants Nos. FIS2005-02309 and UCM-910770. The work of G.H. was supported by an MEC-FPU fellowship.
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