Discrete Moyal-type Representations for a Spin

Details Discrete Moyal-type Representations for a Spin Discrete Moyal-type Representations for a Spin

2000-04-05

arxiv.org/abs/quant-ph/0004022v1

Phys. Rev. A 63 (2001) 012105

Physics

Quantum Physics

23 pages, latex2e, 3 figures

Scientific paper

10.1103/PhysRevA.63.012105

In Moyal's formulation of quantum mechanics, a quantum spin s is described in terms of continuous symbols, i.e. by smooth functions on a two-dimensional sphere. Such prescriptions to associate operators with Wigner functions, P- or Q-symbols, are conveniently expressed in terms of operator kernels satisfying the Stratonovich-Weyl postulates. In analogy to this approach, a discrete Moyal formalism is defined on the basis of a modified set of postulates. It is shown that appropriately modified postulates single out a well-defined set of kernels which give rise to discrete symbols. Now operators are represented by functions taking values on (2s+1)(2s+1) points of the sphere. The discrete symbols contain no redundant information, contrary to the continuous ones. The properties of the resulting discrete Moyal formalism for a quantum spin are worked out in detail and compared to the continuous formalism, and it is illustrated by the example of a spin 1/2.

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