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Regular version of the site

Article

Renormalization of the vacuum angle in quantum mechanics, Berry phase and continuous measurements

Apenko S.M.

The vacuum angle θ renormalization is studied for a toy model of a quantum
particle moving around a ring, threaded by a magnetic flux θ. A novel type
of renormalization group (RG) transformation is introduced by coupling the
particle to an additional slow variable, which may also be viewed as a part of a
device, which ‘measures’ the particle’s position with finite accuracy. Then the
renormalized θ appears as a magnetic flux in the effective action for the slow
‘pointer’ variable. This ‘measurement-induced’ renormalization is shown to
have the same properties as the θ renormalization due to instantons in quantum
field theories and leads to the RG flow diagram, similar to that of the quantum
Hall effect, with observable effective θ vanishing in the limit of small coupling
between the particle and the measuring device.