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GEOMETRIC PHASES IN THE QUANTISATION OF BOSONS AND FERMIONS
Published online by Cambridge University Press: 29 June 2011
Abstract
After reviewing geometric quantisation of linear bosonic and fermionic systems, we study the holonomy of the projectively flat connection on the bundle of Hilbert spaces over the space of compatible complex structures and relate it to the Maslov index and its various generalisations. We also consider bosonic and fermionic harmonic oscillators parametrised by compatible complex structures and compare Berry’s phase with the above holonomy.
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- Copyright © Australian Mathematical Publishing Association Inc. 2011
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