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Spinning string in four-dimensional spacetime as a model of SL(2,$${\mathbb{C}})$$ chiral field with anomaly. I. II. (English. Russian original) Zbl 0701.58061
Theor. Math. Phys. 82, No. 2, 139-145 (1990); 83, No. 1, 377-382 (1990); translation from Teor. Mat. Fiz. 82, No. 2, 199-207 (1990); 83, No. 1, 57-63 (1990).
Summary: In part I, it is shown that the model of open spinning (without Grassmann variables) string in the dimension $$1+3$$ is equivalent to the model of chiral field taking values in the SL(2,$${\mathbb{C}})$$ group and having a fixed anomaly. The Poisson structure of the theory is determined by means of a pair of current algebras with central charge. The action of the model is constructed in terms of the coefficients of the quadratic forms of the string world-sheet. The gauge is used which is a generalization of the standard light cone gauge.
In part II, the construction of part I of relativistically invariant Poisson structure in the string model is completed. It is shown that the relativistic covariance is preserved when the model is quantized.
##### MSC:
 58Z05 Applications of global analysis to the sciences 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
##### Keywords:
spinning string; chiral field; Poisson structure
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##### References:
 [1] L. A. Takhtadzhyan and L. D. Faddeev, The Hamiltonian Approach in the Theory of Solitons [in Russian], Nauka, Moscow (1986). · Zbl 0632.58003 [2] A. G. Reiman and M. A. Semenov-Tyan-Shanskii, Dokl. Akad. Nauk SSSR,251, 1310 (1980). [3] L. Dolan, Phys. Rep.,109, 1 (1984). [4] I. B. Frenkel and V. G. Kac, Inv. Math.,62, 23 (1980). · Zbl 0493.17010 [5] E. Witten, Commun. Math. Phys.,92, 455 (1984). · Zbl 0536.58012 [6] S. P. Novikov, Dokl. Akad. Nauk SSSR,260, 31 (1981). [7] S. V. Talalov, Teor. Mat. Fiz.,79, 41 (1989). [8] V. A. Zhelnorovich, Tensor Representations of Spinors and Spinor Equations [in Russian], State University, Moscow (1979). · Zbl 0449.15021 [9] S. V. Talalov, Teor. Mat. Fiz.,71, 357 (1987). [10] B. M. Barbashov and V. V. Nesterenko, The Model of a Relativistic String in Hadron Physics [in Russian], Énergoatomizdat, Moscow (1987). [11] A. O. Barut and R. Raczka, Theory of Group Representations and Applications, Warsaw (1977). · Zbl 0471.22021 [12] A. K. Pogrebkov and S. V. Talalov, Teor. Mat. Fiz.,70, 342 (1987). [13] M. Wakimoto, Commun. Math. Phys.,104 605 (1986). · Zbl 0587.17009 [14] J. Lepowsky and R. Wilson, Commun. Math. Phys.,62, 43 (1978). · Zbl 0388.17006 [15] G. P. Jorjadze, A. K. Pognebkov, and M. C. Polivanov, J. Phys. A,19, 121 (1986). · Zbl 0597.58044 [16] R. Penrose and R. S. Ward, ?Twistors in flat and curved spacetime,? in: Twistors and Gauge Fields [Russian translation], Mir, Moscow (1983).
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