Dirac quantization of open strings and noncommutativity in branes

Ardalan, F.; Arfaei, H.; Sheikh-Jabbari, M. M.

doi:10.1016/s0550-3213(00)00096-1

Cited by 160 publications

(191 citation statements)

References 28 publications

(66 reference statements)

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“…In fact, for m = 0, Dirac quantization, with the boundary conditions regarded as constraints, has been used as an alternative. The problem that arises then is whether the boundary conditions should be regarded as first or second class, and this is not a trivial choice for they lead to different results [26] [27].…”

Section: Quantizationmentioning

confidence: 99%

Quantization of the open string on plane-wave limits of and non-commutativity outside branes

Horcajada

Ruiz

2008

Nuclear Physics B

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The open string on the plane-wave limit of dS n × S n with constant B 2 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 worldsheet parameter σ, thus extending non-commutativity outside the branes on which the string endpoints may be assumed to move. The Minkowski spacetime limit is smooth and reproduces the results in the literature, in particular non-commutativity gets confined to the endpoints.

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Section: Quantizationmentioning

confidence: 99%

Quantization of the open string on plane-wave limits of and non-commutativity outside branes

Horcajada

Ruiz

2008

Nuclear Physics B

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“…In [10] the authors used the basic principles of Dirac quantization in order to discuss the noncommutativity of the internal coordinates of branes. It was shown that the noncommutativity of the coordinates of the open string-brane system is intrinsic, namely, there is no gauge in which the noncommutativity can be removed.…”

Section: Introductionmentioning

confidence: 99%

“…And the position of noncommutativity is always on the brane. In this work [10] the mixed boundary conditions were treated as the Dirac constraints and the quantization was obtained through the Dirac method without mode expansions.…”

Section: Introductionmentioning

confidence: 99%

“…The authors proposed that the arbitrariness of the regularization can lead to different results in the literature. Therefore, trying to make a comparison, we can say that in [10] the nontrivial boundary condition in the presence of the B-field modify the canonical commutation relations and leads to noncommutativity on D-brane world volume. In [12] the authors examine the symplectic form obtained in terms of the mode expansion of the classical solutions.…”

Section: Introductionmentioning

confidence: 99%

“…The main difference between [10,12] and [17] is the choice of the nonvanishing multiplier in the primary Hamiltonian. The results disclose no secondary constraints and the single primary constraint itself forms the second class constraint algebra.…”

Section: Introductionmentioning

confidence: 99%

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Open string with a backgroundBfield as the first order mechanics, noncommutativity, and soldering formalism

et al. 2007

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To study noncommutativity properties of the open string with constant B-field we construct a mechanical action which reproduces classical dynamics of the string sector under consideration. It allows one to apply the Dirac quantization procedure for constrained systems in a direct and unambiguous way. The mechanical action turns out to be the first order system without taking the strong field limit B −→ ∞. In particular, it is true for zero mode of the string coordinate which means that the noncommutativity is intrinsic property of this mechanical system. We describe the arbitrariness in the relation existent between the mechanical and the string variables and show that noncommutativity of the string variables on the boundary can be removed. It is in correspondence with the result of Seiberg and Witten on relation among noncommutative and ordinary Yang-Mills theories. The recently developed soldering formalism helps us to establish a connection between the original open string action and the Polyakov action.

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Central charge contribution to noncommutativity

Nikolić

Sazdović

2008

Fortschritte der Physik

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In the presence of antisymmetric Kalb‐Ramond field Bμν Dp‐brane, to which string endpoints are attached, is a noncommutative manifold. Adding linear dilaton field, Φ(x) = Φ0 + aμ xμ, the coordinate in the direction of dilaton gradient, xc = aμ xμ, becomes commutative, while the world‐sheet conformal factor F is a new noncommutative variable. In this article we demonstrate different approach to realization of quantum conformal invariance. We introduce Liouville action in such a way that world‐sheet conformal factor F does not spoil quantum conformal invariance and theory depends on arbitrary parameter, central charge c. Particular relations between background fields produce local gauge symmetries, which transform some of the Neumann into the Dirichlet boundary conditions decreasing the dimensionality of Dp‐brane.We introduce one methodological improvement regarding derivation of boundary conditions. Canonical Hamiltonian as a time translation generator must have well defined derivatives in coordinates and momenta. From this requirement we obtain boundary conditions directly in terms of canonical variables.

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Dirac quantization of open strings and noncommutativity in branes

Abstract: We apply the Dirac bracket quantization to open strings attached to branes in the presence of background antisymmetric field and recover an inherent noncommutativity in the internal coordinates of the brane.

Cited by 160 publications

References 28 publications

Quantization of the open string on plane-wave limits of and non-commutativity outside branes

Quantization of the open string on plane-wave limits of and non-commutativity outside branes

Open string with a backgroundBfield as the first order mechanics, noncommutativity, and soldering formalism

Central charge contribution to noncommutativity

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