Disclination in Lorentz spacetime (Q2724829)

The disclination is a kind of topological defect caused by the insertion of a solid angle into the flat spacetime. Its density may be expressed as NEWLINE\[NEWLINE\theta^{ab}= {1\over 2}R^\lambda_{\mu\nu \sigma}e^a_\lambda e^{\sigma b}dx^\mu \wedge dx^\nu= -F^{ab},NEWLINE\]NEWLINE where \(R\) is the Riemannian curvature and \(F\) is a gauge field tensor. The size of the disclination is represented by means of projections along an antisymmetric tensor field \(\varphi^{ab}\), namely \(\Omega=\int_\Sigma \theta^{ab} \varphi^{ab}\). The author shows how the spacetime disclination can be described in terms of a Dirac spinor, and characterized by the Brouwer degree and the Hopf index.