Reply to Boglione and Pennington

Lee, W.; Weingarten, D.

doi:10.1103/physrevd.62.038502

Cited by 110 publications

(245 citation statements)

References 9 publications

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“…To achieve this, there were proposed rather radical modifications [8,11] of the Dirac procedure for constrained systems. There is some discrepancy among the results obtained in different approaches, which was discussed in [8,9,10,11,12,16,17]. Let us talk about these issues for a while in order to put our work in a perspective.…”

Section: Introductionmentioning

confidence: 99%

“…According to the Darboux theorem, one can equally take as the starting point any nondegenerate closed two-form and then try to define a Hamiltonian from the condition that corresponding equations of motion are equivalent to the initial ones. Turning to our case (16), (17) it will be sufficiently to consider the brackets (25) with some antisymmetric nondegenerate constant matrices E and A. From the condition that the dynamics (8) is reproduced in this formulation one finds…”

Section: Hamiltonian Formulation For the Open String With A B-fieldmentioning

confidence: 99%

“…Transition from configuration to phase space description is not unique procedure since one needs to define simultaneously the bracket and the Hamiltonian. One possibility is to start from the Poisson bracket, then exact expression for the Hamiltonian is known for a general case [19,23] [16,20]. According to the Darboux theorem, one can equally take as the starting point any nondegenerate closed two-form and then try to define a Hamiltonian from the condition that corresponding equations of motion are equivalent to the initial ones.…”

Section: Hamiltonian Formulation For the Open String With A B-fieldmentioning

confidence: 99%

“…To understand the dynamics of D-brane with a Bfield, the author in [16] used the canonical quantization. With background field B one can obtain a mixed boundary condition, which generates an infinite number of secondary second-class constraints.…”

Section: Introductionmentioning

confidence: 99%

“…With background field B one can obtain a mixed boundary condition, which generates an infinite number of secondary second-class constraints. These constraints were solved explicitly in [16] in order to obtain a simple Hamiltonian for the open string in the D-brane background. The Hamiltonian found was a free Hamiltonian for an open string in spacetime.…”

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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