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We apply geometric phase ideas to coherent states to shed light oninterference phenomenon in the phase space description of continuous variableCartesian quantum systems. In contrast to Young's interference characterized bypath lengths, phase space interference turns out to be determined by areas. Themotivating idea is Pancharatnam's concept of "being in phase" for Hilbert spacevectors. Applied to the overcomplete family of coherent states, we are led topreferred one-dimensional integral representations for various states ofphysical significance, such as the position, momentum, Fock states and thesqueezed vacuum. These are special in the sense of being "in-phasesuperpositions". Area considerations emerge naturally within a fully quantummechanical context. Interestingly, the Q-function is maximized along the lineof such superpositions. We also get a fresh perspective on the Bohr-Sommerfeldquantization condition. Finally, we use our exact integral representations toobtain asymptotic expansions for state overlaps and matrix elements, leading tophase space area considerations similar to the ones noted earlier in theseminal works of Schleich, Wheeler and collaborators, but now from theperspective of geometric phase.

Geometric Phase as the Key to Interference in Phase Space : Integral Representations for States and Matrix Elements