Phase operator for the photon, an index theorem, and quantum anomaly

Details Phase operator for the photon, an index theorem, and quantum anomaly Phase operator for the photon, an index theorem, and quantum anomaly

1995-09-23

arxiv.org/abs/hep-th/9509128v1

Physics

High Energy Physics

High Energy Physics - Theory

To be published in the Proceedings of International Symposium on Foundations of Quantum Mechanics, Tokyo, 1995

Scientific paper

An index relation $dim\ ker\ a - dim\ ker\ a^{\dagger} = 1$ is satisfied by the creation and annihilation operators $a^{\dagger}$ and $a$ of a harmonic oscillator. Implications of this analytic index on the possible form of the phase operator are discussed. A close analogy between the present phase operator problem and chiral anomaly in gauge theory, which is associated with Atiyah-Singer index theorem, is emphasized.

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