Tomasz Trześniewski

Point Particles and Quantum Gravity

The classical theory of gravitation in 2 + 1 dimensions is encouraging in its simplicity, characterized above all by the absence of propagating local degrees of freedom. In a sense, as a consequence it can be formulated as the Cherns-Simons gauge theory, which symmetry may however be broken by non-trivial topology of spacetime or more physically { by point particles. Such an approach is naturally suited for one of the numerous quantisation schemes applied to (2 + 1)-dimensional gravity, the so-called deformation quantisation. Inspired by this, one may wish to explore whether something similar could occur in 3 + 1 dimensions. Indeed, using the BF theory we are able to express gravitation as a perturbative expansion around the topological background, the Chern-Simons theory at the boundary of spacetime, to which particles are added as topological defects.