Normal ordering and non(anti)commutativity in open super strings

Gangopadhyay, Sunandan; Hazra, Arindam Ghosh

doi:10.1103/physrevd.75.065026

Cited by 9 publications

(12 citation statements)

References 25 publications

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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%

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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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Section: Twisted Hopf Algebra In B Field Backgroundmentioning

confidence: 90%

“…(9) This shows that the twist element F is a coboundary and thus it is trivial in the Hopf algebra cohomology. Consequently, there is an isomorphism between the Hopf algebrasĤ and H F and the module algebrasÂ and A F , respectively, which can be summarized as:…”

Section: Normal Ordering and Path Integralsmentioning

confidence: 94%

Noncommutative geometry in string and twisted Hopf algebra of diffeomorphism

Watamura

2010

Gen Relativ Gravit

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“…where the form of the antiperiodic delta function (15) has been used. This completes the analysis of the fermionic algebra for the NS BC(s).…”

Section: Fermionic Sectormentioning

confidence: 99%

“…Andrade et al [11] took the BC(s) as second class constraint and project the original coordinates on the constraint surface to recover a set of unconstrained string coordinates. Very recently the Faddeev-Jackiw symplectic formalism and a conformal field theoretic approach have been used to obtain the NC structure in [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

String Non(anti)commutativity for Neveu-Schwarz Boundary Conditions

Chatterjee

Gangopadhyay

Hazra³

et al. 2008

Int J Theor Phys

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The appearance of non(anti)commutativity in superstring theory, satisfying the Neveu-Schwarz boundary conditions is discussed in this paper. Both an open free superstring and also one moving in a background antisymmetric tensor field are analyzed to illustrate the point that string non(anti)commutativity is a consequence of the nontrivial boundary conditions. The method used here is quite different from several other approaches where boundary conditions were treated as constraints. An interesting observation of this study is that, one requires that the bosonic sector satisfies Dirichlet boundary conditions at one end and Neumann at the other in the case of the bosonic variables X μ being antiperiodic. The non(anti)commutative structures derived in this paper also leads to the closure of the super constraint algebra which is essential for the internal consistency of our analysis.

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“…As a quantization, this twisted Hopf algebra structure corresponds to a new normal ordering in the operator formulation, which was studied in Refs. [19,20,21,22]. As a symmetry, it represents a twisted symmetry including space-time diffeomorphisms.…”

Section: Introductionmentioning

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.

show abstract

Normal ordering and non(anti)commutativity in open super strings

Cited by 9 publications

References 25 publications

Noncommutative geometry in string and twisted Hopf algebra of diffeomorphism

Noncommutative geometry in string and twisted Hopf algebra of diffeomorphism

String Non(anti)commutativity for Neveu-Schwarz Boundary Conditions

Twist quantization of string andBfield background

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