Ennio Gozzi

On removing Berry's phase

Abstract In this paper we show that the Berry phase can always be cancelled by a unitary transformation if the space of external parameters is appropriately restricted, but it simply reappears as part of the dynamical phase. Moreover the overall extra geometrical phase measured in experiments is unambiguous and retains its geometrical character.

On the removability of Berry's phase

The authors present a thorough analysis of the removability of the Berry phase. They show that for any system they can, by properly restricting the parameter space turn the geometrical phase into an extra shift of the dynamical one. However, this extra shift in the dynamical phase retains its truly geometrical character. The removability is thus only apparent and the geometrical phase can still be measured in interference experiments, as indeed has already been done several times.

BRST quantization, IOSp (D, 2|2) invariance and the PCT theorem

Abstract In this paper we formulate the BRST quantization of the spinless relativistic point particle without restricting the parameter space to one fundamental domain of the modular group. Modular invariance is instead enforced by a constraint on the physical subspace of the Hilbert space. The second-quantized theory has then a manifest IOSp( D , 2|2) invariance. Studying this symmetry we find that a special element of the SO( D , 2) subgroup of IOSp( D , 2|2) can be identified which induces the PCT transformation on the physical subspace. Using this, the PCT theorem is derived as a simple consequence of the IOSp( D , 2|2) invariance, thus confirming the relevant role of this graded symmetry. The subgroup SO( D , 2) seems to play a central role also in another respect: by requiring covariance of the BRST quantization with respect to it, and not just invariance with respect to the Lorentz group SO( D − 1,1) the overall IOSp( D , 2|2) symmetry is generated.