Normal ordering and boundary conditions in open bosonic strings

Braga, Nelson R. F.; Carrion, H. L.; Godinho, Cresus F. L.

doi:10.1063/1.1914727

Cited by 12 publications

(26 citation statements)

References 13 publications

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“…Twisting by F 1 directly, we obtain the normal ordered module algebraÂ 1 . The same normal ordering in the context of operator formalism is given in the literature [15,16,17,18]. Here we decompose F 1 in two different ways [2].…”

Section: Twist Quantization With B Fieldmentioning

confidence: 82%

Twist Quantization of String and Hopf Algebraic Symmetry

Asakawa

Watamura²

2010

SIGMA

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Abstract. We describe the twist quantization of string worldsheet theory, which unifies the description of quantization and the target space symmetry, based on the twisting of Hopf and module algebras. We formulate a method of decomposing a twist into successive twists to analyze the twisted Hopf and module algebra structure, and apply it to several examples, including finite twisted diffeomorphism and extra treatment for zero modes.

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Section: Twist Quantization With B Fieldmentioning

confidence: 82%

Twist Quantization of String and Hopf Algebraic Symmetry

Asakawa

Watamura²

2010

SIGMA

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“…In fact, the normal ordering defined by (21) coincides with that proposed in [6][7][8][9]. There, this normal ordering was introduced such that a normal ordered operator like • •X μ (z)X ν (w) • • satisfies not only the equation of motion, but also the mixed boundary condition as an operator relation.…”

Section: Twisted Hopf Algebra In B Field Backgroundmentioning

confidence: 90%

Noncommutative geometry in string and twisted Hopf algebra of diffeomorphism

Watamura

2010

Gen Relativ Gravit

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We discuss the Hopf algebra structure in string theory and present the twist quantization as a unified formulation of the world sheet quantization of the string and the symmetry of the target spacetime. Applying it to the case with a nonzero B-field background, we explain a method to decompose the twist into two successive twists. There are two different possibilities of decomposition: The first is a natural decomposition from the viewpoint of the twist quantization, leading to a new type of twisted Poincaré symmetry. The second decomposition reveals the relation of our formulation to the twisted Poincaré symmetry on the Moyal type noncommutative space.

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“…In fact, the normal ordering defined by (3.9) coincides with that proposed in Refs. [19,20,21,22]. There, this normal ordering was introduced such that a normal ordered operator like •…”

Section: Twist Quantization With B Fieldmentioning

confidence: 99%

Twist quantization of string andBfield background

Asakawa

Mori

Watamura

2009

J. High Energy Phys.

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In a previous paper, we investigated the Hopf algebra structure in string theory and gave a unified formulation of the quantization of the string and the spacetime symmetry. In this paper, this formulation is applied to the case with a nonzero B-field background, and the twist of the Poincaré symmetry is studied. The Drinfeld twist accompanied by the B-field background gives an alternative quantization scheme, which requires a new normal ordering. In order to obtain a physical interpretation of this twisted Hopf algebra structure, we propose a method to decompose the twist into two successive twists and we give two different possibilities of decomposition. The first is a natural decomposition from the viewpoint of the twist quantization, leading to a new type of twisted Poincaré symmetry. The second decomposition reveals the relation of our formulation to the twisted Poincaré symmetry on the Moyal type noncommutative space.

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Normal ordering and boundary conditions in open bosonic strings

Cited by 12 publications

References 13 publications

Twist Quantization of String and Hopf Algebraic Symmetry

Twist Quantization of String and Hopf Algebraic Symmetry

Noncommutative geometry in string and twisted Hopf algebra of diffeomorphism

Twist quantization of string andBfield background

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