Journal of Mathematical Physics
American Institute of Physics
The degree to which the phase space of a closed bosonic string carries a representation of the two‐dimensional diffeomorphism group Diff(M) is investigated. In particular, homomorphic mappings from the associated Lie algebra diff(M) into the Poisson algebra of functions on three natural phase spaces associated with the string are constructed. Two of these spaces are extended phase spaces based on the conformal and harmonic gauges, respectively. The third space is essentially the original phase space; the homomorphism in this case relies on the validity of the light‐cone gauge. Homomorphisms from diff(M) into the extended phase spaces of the Batalin–Fradkin–Vilkovisky formalism are also constructed. While the methods used to represent diff(M) cannot be extended to represent all of Diff(M), the phase spaces do carry a representation of the subgroup of conformal isometries. It is argued that this subgroup is sufficiently large to serve as the dynamical group for the string. The implications of this work for a true Dirac quantization of the string via operator representations of diff(M) are discussed.
K.V. Kuchař and C.G. Torre, “World sheet diffeomorphisms and the canonical string,” Journal of Mathematical Physics, vol. 30, 1989, p. 1769.