Canonical Quantization of Open String and Noncommutative Geometry

Abstract

We perform canonical quantization of open strings in the $D$-brane background with a $B$-field. Treating the mixed boundary condition as a primary constraint, we get a set of secondary constraints. Then these constraints are shown to be equivalent to orbifold conditions to be imposed on normal string modes. These orbifold conditions are a generalization of the familiar orbifold conditions which arise when we describe open strings in terms of closed strings. Solving the constraints explicitly, we obtain a simple Hamiltonian for the open string, which reveals the nature of noncommutativity transparently.

14 pages, RevTex, added references

References in corpus (5)

• String Theory and Noncommutative Geometry
• D-branes and Deformation Quantization
• Large N Limit of Non-Commutative Gauge Theories
• Non-Commutative Yang-Mills and the AdS/CFT Correspondence
• Morita equivalence and T-duality (or B versus $\Theta$)

Cited by in corpus (28)

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• Hamiltonian systems with boundaries
• Hamiltonian treatment of linear field theories in the presence of boundaries: a geometric approach
• Running couplings and triviality of field theories on non-commutative spaces
• Canonical approach to the closed string noncommutativity
• Tachyon Condensation and Open String Field theory
• Gauge symmetries decrease the number of Dp-brane dimensions
• Gauge symmetries decrease the number of Dp-brane dimensions. II. Inclusion of the Liouville term
• Kontsevich product and gauge invariance
• Noncommutativity in weakly curved background by canonical methods
• Type I background fields in terms of type IIB ones
• BFT embedding of noncommutative D-brane system
• Non-commutativity parameters depend not only on the effective coordinate but on its T-dual as well
• Physics-to-gauge conversion at black hole horizons
• High-Temperature Effective Potential of Noncommutative Scalar Field Theory: Reduction of Degree of Freedom by Noncommutativity
• Fermionic T-duality and momenta noncommutativity
• Directly from $H$-flux to the family of three nonlocal $R$-flux theories
• Open string with a background B-field as the first order mechanics, noncommutativity and soldering formalism
• The Reduced Phase Space of An Open String in The Background B-Field
• Noncommutative Open String: Neutral and Charged
• Noncommutativity relations in type IIB theory and their supersymmetry
• Dirichlet boundary conditions in type IIB superstring theory and fermionic T-duality
• String Field Theory and Perturbative Dynamics of Noncommutative Field Theory
• Quons in a Quantum Dissipative System
• T-duality of a bosonic string in a weakly curved space-time
• Relations between Non-Commutative and Commutative Spacetime