×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
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], √Čnergoatomizdat, 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).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.