We study the phase space structure and the quantization of a pointlike particle in (2 + 1)-dimensional gravity. By adding boundary terms to the first-order Einstein-Hilbert action, and removing all redundant gauge degrees of freedom, we arrive at a reduced action for a gravitating particle in 2+1 dimensions, which is invariant under Lorentz transformations and a group of generalized translations. The momentum space of the particle turns out to be the group manifold SL(2). Its position coordinates have non-vanishing Poisson brackets, resulting in a non-commutative quantum spacetime. We use the representation theory of SL(2) to investigate its structure. We find a discretization of time, and some semi-discrete structure of space. An uncertainty relation forbids a fully localized particle. The quantum dynamics is described by a discretized Klein-Gordon equation.

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Despite a significant advance in microsurgery of the parasagittal brain meningiomas the problem of its surgical treatment is not closed at the present time. This is due to the fact that parasagittal meningiomas can ingrow to the sinus lumen. In this cases the possibility of tumor resection using conventional techniques is limited. Attempts at the tumor radical removal lead to a massive operating blood loss, a stable severe neurological deficit and decrease the quality of life. This results in high recurrence rate of parasagittal meningiomas also. The paper presents the results of ND-YAG laser use in the removal of parasagittal meningiomas with assessment of its application efficacy as compared with conventional techniques.