Spinning string in four-dimensional spacetime as a model of $SL(2,\mathbb C)$ chiral field with anomaly. I

It is shown that the model of an open spinning (without Grassmann variables) string in dimension $\mathscr D=1+3$ is equivalent to the model of a chiral field that takes values in the group $SL(2,\mathbb C)$ and has a fixed anomaly. The Poisson structure of the theory is determined by 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 world surface of the string. A gauge that generalizes the standard light-cone gauge is used.