Geodesic
Twist Quantization of String and Hopf Algebraic Symmetry
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010)

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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.
Keywords: string theory; qunatization; Hopf algebra; Drinfeld twist. 
Tsuguhiko Asakawa; Satoshi Watamura. Twist Quantization of String and Hopf Algebraic Symmetry. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a67/
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     author = {Tsuguhiko Asakawa and Satoshi Watamura},
     title = {Twist {Quantization} of {String} and {Hopf} {Algebraic} {Symmetry}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a67/}
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[1] Asakawa T., Mori M., Watamura S., “Hopf algebra symmetry and string theory”, Progr. Theoret. Phys., 120 (2008), 659–689, arXiv: 0805.2203 | DOI | Zbl

[2] Asakawa T., Mori M., Watamura S., “Twist quantization of string and $B$ field background”, J. High Energy Phys., 2009:4 (2009), 117, 25 pp., arXiv: 0811.1638 | DOI | MR

[3] Drinfeld V. G., “Quasi-Hopf algebras”, Leningrad Math. J., 1 (1990), 1419–1457 | MR

[4] Chaichian M., Kulish P. P., Nishijima K., Tureanu A., “On a Lorentz-invariant interpretation of noncommutative space-time and its implications on noncommutative QFT”, Phys. Lett. B, 604 (2004), 98–102, arXiv: hep-th/0408069 | DOI | MR

[5] Koch F., Tsouchnika E., “Construction of $\theta$-Poincaré algebras and their invariants on $\mathcal M_\theta$”, Nuclear Phys. B, 717 (2005), 387–403, arXiv: hep-th/0409012 | DOI | MR | Zbl

[6] Aschieri P., Blohmann C., Dimitrijević M., Meyer F., Schupp P., Wess J., “A gravity theory on noncommutative spaces”, Classical Quantum Gravity, 22 (2005), 3511–3532, arXiv: hep-th/0504183 | DOI | MR | Zbl

[7] Watamura S., “Noncommutative geometry in string and twisted Hopf algebra of diffeomorphism”, Gen. Relativity Gravitation | DOI

[8] Aschieri P., Lizzi F., Vitale P., “Twisting all the way: from classical mechanics to quantum fields”, Phys. Rev. D, 77 (2008), 025037, 16 pp., arXiv: 0708.3002 | DOI | MR

[9] Majid S., Foundations of quantum group theory, Cambridge University Press, Cambridge, 1995 | MR | Zbl

[10] Polchinski J., String theory, Cambridge University Press, Cambridge, 1998

[11] Álvarez-Gaumé L., Meyer F., Vázquez-Mozo M. A., “Comments on noncommutative gravity”, Nuclear Phys. B, 753 (2006), 92–117, arXiv: hep-th/0605113 | DOI | MR | Zbl

[12] Fradkin E. S., Tseytlin A. A., “Nonlinear electrodynamics from quantized strings”, Phys. Lett. B, 163 (1985), 123–130 | DOI | MR | Zbl

[13] Callan C. G., Lovelace C., Nappi C. R., Yost S. A., “String loop corrections to beta functions”, Nuclear Phys. B, 288 (1987), 525–550 | DOI | MR

[14] Abouelsaood A., Callan C. G., Nappi C. R., Yost S. A., “Open strings in background gauge fields”, Nuclear Phys. B, 280 (1987), 599–624 | DOI | MR

[15] Braga N. R. F., Carrion H. L., Godinho C. F. L., “Normal ordering and boundary conditions in open bosonic strings”, J. Math. Phys., 46 (2005), 062302, 5 pp., arXiv: hep-th/0412075 | DOI | MR | Zbl

[16] Braga N. R. F., Carrion H. L., Godinho C. F. L., “Normal ordering and boundary conditions for fermionic string coordinates”, Phys. Lett. B, 638 (2006), 272–274, arXiv: hep-th/0602212 | DOI | MR

[17] Chakraborty B., Gangopadhyay S., Hazra A. G., “Normal ordering and noncommutativity in open bosonic strings”, Phys. Rev. D, 74 (2006), 105011, 6 pp., arXiv: hep-th/0608065 | DOI | MR

[18] Gangopadhyay S., Hazra A. G., “Normal ordering and non(anti)commutativity in open super strings”, Phys. Rev. D, 75 (2007), 065026, 6 pp., arXiv: hep-th/0703091 | DOI | MR

[19] Seiberg N., Witten E., “String theory and noncommutative geometry \”, J. High Energy Phys., 1999:9 (1999), 032, 93 pp., arXiv: hep-th/9908142 | DOI | MR

[20] Oeckl R., “Untwisting noncommutative $\mathbb R^d$ and the equivalence of quantum field theories”, Nuclear Phys. B, 581 (2000), 559–574, arXiv: hep-th/0003018 | DOI | MR | Zbl

[21] Watts P., Derivatives and the role of the Drinfeld twist in noncommutative string theory, arXiv: hep-th/0003234