The RST model is augmented by the addition of a scalar field and a boundary term so that it is well-posed and local. Expressing the RST action in terms of the ADM formulation, the constraint structure can be analysed completely. It is shown that from the view point of local field theories, there exists a hidden dynamical field 1 in the RST model. Thanks to the presence of this hidden dynamical field, we can reconstruct the closed algebra of the constraints which guarantee the general invariance of the RST action. The resulting stress tensors TSigma Sigma are recovered to be true tensor quantities. Especially, the part of the stress tensors for the hidden dynamical field 1 gives the precise expression for tSigma . At the quantum level, the cancellation condition for the total central charge is reexamined. Finally, with the help of the hidden dynamical field 1, the fact that the semi-classical static soluti on of the RST model has two independent parameters (P,M), whereas for the classical CGHS model there is only one, can be explained.
The significance of zero modes in the path-integral quantization of some solitonic models is investigated. In particular a Skyrme-like theory with topological vortices in (1 + 2) dimensions is studied, and with a BRST invariant gauge fixing a well defined transition amplitude is obtained in the one loop approximation. We also present an alternative method which does not necessitate evoking the time-dependence in the functional integral, but is equivalent to the original one in dealing with the quantization in the background of the static classical solution of the non-linear field equations. The considerations given here are particularly useful in - but also limited to -the one-loop approximation.
The Lagrangian field-antifield formalism of Batalin and Vilkovisky (BV) is used to investigate the application of the collec- tive coordinate method to soliton quantisation. In field theories with soliton solutions, the Gaussian fluctuation operator has zero modes due to the breakdown of global symmetries of the Lagrangian in the soliton solutions. It is shown how Noether identities and local symmetries of the Lagrangian arise when collective coordinates are introduced in order to avoid divergences related to these zero modes. This transformation to collective and fluctuation degrees of freedom is interpreted as a canonical transformation in the symplectic field-antifield space which induces a time-local gauge symmetry. Separating the corresponding Lagrangian path integral of the BV scheme in lowest order into harmonic quantum fluctuations and a free motion of the collective coordinate with the classical mass of the soliton, we show how the BV approach clarifies the relation between zero modes, collective coordinates, gauge invariance and the center- of-mass motion of classical solutions in quantum fields. Finally, we apply the procedure to the reduced nonlinear O(3) oe-model.^L