Dirac fermions on rotating space-times

Quantum states of Dirac fermions at zero or finite temperature are investigated using the point-splitting method in Minkowski and anti-de Sitter space-times undergoing rotation about a fixed axis.

In the Minkowski case, analytic expressions presented for the thermal expectation values (t.e.v.s) of the fermion condensate, parity violating neutrino current and stress-energy tensor show that thermal states diverge as the speed of light surface (SOL) is approached. The divergence is cured by enclosing the rotating system inside a cylinder located on or inside the SOL, on which spectral and MIT bag boundary conditions are considered.

For anti-de Sitter space-time, renormalised vacuum expectation values are calculated using the Hadamard and Schwinger-de Witt methods. An analytic expression for the bi-spinor of parallel transport is presented, with which some analytic expressions for the t.e.v.s of the fermion condensate and stress-energy tensor are obtained. Rotating states are investigated and it is found that for small angular velocities $\Omega$ of the rotation, there is no SOL and the thermal states are regular everywhere on the space-time. However, if $\Omega$ is larger than the inverse radius of curvature of adS, an SOL forms and t.e.v.s diverge as inverse powers of the distance to it.