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.


58Z05 Applications of global analysis to the sciences
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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