Topology of solutions of the Liouville equation
Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.
dg-ga↗
arXiv subjects
Wlodzimierz Piechocki
Publications and source records attributed to Wlodzimierz Piechocki.
Topology of the set of smooth solutions to the Liouville equation
We prove that the space of smooth initial data and the set of smooth solutions of the Liouville equation are homeomorphic.
dg-ga↗
Dynamical Ambiguities in Singular Gravitational Field
We consider particle dynamics in singular gravitational field. In 2d spacetime the system splits into two independent gravitational systems without singularity. Dynamical integrals of each system define $sl(2,R)$ algebra, but the corresponding symmetry transformations are not defined globally. Quantization leads to ambiguity. By including singularity one can get the global $SO(2.1)$ symmetry. Quantization in this case leads to unique quantum theory.
gr-qc↗
Relativistic Particle in the Liouville Field
A model of a relativistic particle moving in the Liouville field is investigated. Symmetry group of the system is $SL(2,R)/Z_2$. The corresponding dynamical integrals describe full set of classical trajectories. Dynamical integrals are used for the gauge-invariant Hamiltonian reduction. The new scheme is proposed for quantization of the reduced system. Obtained quantum system reproduces classical symmetry. Physical aspects of the model are discussed.
hep-th↗