An attempt towards the definition of the phase of quantum oscillators

Yurii I. Vorontsov

周鹏

The study of the quantized field phase dates back to Diracs definition of the phase operator which came from a polar decomposition of the annihilation operator following a simple analogy with the phase of a classical harmonic oscillator, according to the usual procedure of quantization. Unfortunately, this approach causes inconsistency. Some people attempted to investigate the phase properties from various angles after Dirac.

Michael Hartley Freedman

I would claim that we do not have a suitably general definition of what a topological phase is, or more importantly, any robust understanding of how to enter one even in the world of mathematical models. The latter is, of course, the more important issue and the main subject of this note. But a good definition can sharpen our thinking and a poor definition can misdirect us. I will not attempt a final answer here but merely comment on the strengths and weaknesses of possible definitions and argue for some flexibility. In particular, I describe a rather simple class of ``quantum gravity'' models which are neither lattice nor field theoretic but appear to contain strong candidates for topological phases.

R. Shepard Scott

Vlasta Peřinová, A. Lukš

It is familiar that a well behaved operator of the harmonic oscillator phase does not exist. Therefore, Turski's phase operator and the operator of Garrison and Wong may be at most defined in an interesting fashion and yield useful quantum expectation values. In this paper we touch on a recent incomplete definition of a phase operator which has also failed in the respect that it can be completed only to a definition of an 'incomplete' phase operator. We discuss, however, a possibility of completion of the definition and a relationship to the phase operator from an s-parametrized quasidistribution.

P. Tsilimigras, Loucas C. Papaloucas