Abstract
We develop a treatment of bosonic strings on a general curved background in which the volume element and the coordinates of the worldsheet are related in a similar way as canonically conjugate quantities in mechanics. The resultant formalism is a particular variant of the multi-phase-space approach to classical field theory put forward by Kijowski, Tulczyjew, and others. We study conservation laws within this framework and find that all conserved quantities are related to point symmetries, i.e., isometries of the underlying spacetime. Thus, the symmetries of relativistic mechanics coming from Killing tensors have no analogue here. We furthermore deduce from the present scheme the covariant version of the usual phase space.
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Beig, R. Classical geometry of bosonic string dynamics. Int J Theor Phys 30, 211–224 (1991). https://doi.org/10.1007/BF00670714
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DOI: https://doi.org/10.1007/BF00670714