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Physically Acceptable Solutions of an Eigenvalue Equation in Deformation Quantization

Jaromir Tosiek

Springer eBooksSep 28, 20120 citations

States in Deformation Quantization

Jaromir Tosiek

Trends in mathematicsJan 1, 20140 citations

Least uncertainty principle in deformation quantization

Murray Gerstenhaber

Deformation quantization generally produces families of cohomologically equivalent quantizations of a single physical system. We conjecture that the physically meaningful ones (i) allow enough observable energy distributions, i.e., ones for which no pure quantum state has negative probability, and (ii) reduce the uncertainty in the probability distribution of the resulting quantum states. For the simple harmonic oscillator this principle selects the classic Groenewold-Moyal (or Weyl) product on phase space while for the free particle, in which there is no real quantization, all cohomologically equivalent quantizations are equally good.Deformation quantization generally produces families of cohomologically equivalent quantizations of a single physical system. We conjecture that the physically meaningful ones (i) allow enough observable energy distributions, i.e., ones for which no pure quantum state has negative probability, and (ii) reduce the uncertainty in the probability distribution of the resulting quantum states. For the simple harmonic oscillator this principle selects the classic Groenewold-Moyal (or Weyl) product on phase space while for the free particle, in which there is no real quantization, all cohomologically equivalent quantizations are equally good.

Journal of Mathematical PhysicsFeb 1, 20074 citations

Application of the Canonical Theory of Mixed State to the Description of Bound State of the Nucleus. II: Schematic Model and Physical Ingredients of Constraints

A. Kuriyama, João da Providência, M. Yamamura

The theory developed in Part I of this series of papers is adapted to a schematic model, the Lipkin model. In this case, we can introduce a set of canonical variables satisfying automatically the constraints and obtain an exact boson representation of the Lipkin model after a canonical quantization. However, when the constraints themselves are also quantized, the physical ingredients of the constraints are revealed under a completely different perspective.

Progress of Theoretical PhysicsApr 1, 19920 citations

On A Mathematical Theory of Quantization

Hiroyasu Koshimizu

대한전자공학회 워크샵Feb 1, 20030 citations

Application of the Canonical Theory of Mixed State to the Description of Bound State of the Nucleus. II

A. Kuriyama, João da Providência, Masatoshi Yamamura

The theory developed in Part I of this series of papers is adapted to a schematic model, the Lipkin model. In this case, we can introduce a set of canonical variables satisfying automatically the constraints and obtain an exact boson representation of the Lipkin model after a canonical quantization. However, when the constraints themselves are also quantized, the physical ingredients of the constraints are revealed under a completely different perspective.

Progress of Theoretical PhysicsApr 1, 19920 citations

Deformation theory and quantization. II. Physical applications

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