Massive spinor fields in flat spacetimes with nontrivial topology

Abstract

The vacuum expectation value of the stress-energy tensor is calculated for spin $\frac{1}{2}$ massive fields in several multiply connected flat space-times. We examine the physical effects of topology on manifolds such as ${R}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$, ${R}^{2}\ifmmode\times\else\texttimes\fi{}{T}^{2}$, ${R}^{1}\ifmmode\times\else\texttimes\fi{}{T}^{3}$, the M\"obius strip, and the Klein bottle. We find that the spinor vacuum stress tensor has the opposite sign to, and twice the magnitude of, the scalar tensor in orientable manifolds. Extending the above considerations to the case of Misner spacetime, we calculate the vacuum expectation value of spinor stress-energy tensor in this space and discuss its implications for the chronology protection conjecture.