Phase operator for the photon, an index theorem, and quantum anomaly
Abstract
Description
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.
To be published in the Proceedings of International Symposium on Foundations of Quantum Mechanics, Tokyo, 1995
To be published in the Proceedings of International Symposium on Foundations of Quantum Mechanics, Tokyo, 1995