J an 2 00 1 Relativistic Aharonov - Casher Phase in Spin One

The Aharonov-Casher (AC) phase is calculated in relativistic wave equations of spin one. The AC phase has previously been calculated from the Dirac-Pauli equation using a gauge-like technique [1, 2]. In the spin-one case, we use Kemmer theory (a Dirac-like particle theory) to calculate the phase in a similar manner. However the vector formalism, the Proca theory, is more widely known and used. In the presence of an electromagnetic field, the two theories are ‘equivalent’ and may be transformed into one another. We adapt these transformations to show that the Kemmer theory results apply to the Proca theory. Then we calculate the Aharonov-Casher phase for spin-one particles directly in the Proca formalism.