Homogeneous star products and closed integral formulas

Tounsi, Khaled

doi:10.2748/tmj/1294170346

Cited by 2 publications

(2 citation statements)

References 17 publications

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“…Such star-product was already considered in [22] from the perspective of formal deformation quantization. Note, that since f and g have supports in G × O the ⋆-product of f and g is a well defined function on M .…”

Section: Star-product On F (M)mentioning

confidence: 99%

“…Worth noting are papers [19,20] where authors introduce a star-product on the cotangent bundle of a Lie group in terms of a formal power series in . Also in [21,22] are studied homogeneous star-products on cotangent bundles of Lie groups, which are characterized in terms of integral formulas. More often starproducts are investigated on duals of Lie algebras (see e.g.…”

Section: Introductionmentioning

confidence: 99%

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Deformation quantization on the cotangent bundle of a Lie group

Domański¹

2018

Preprint

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We develop a complete theory of non-formal deformation quantization on the cotangent bundle of a weakly exponential Lie group. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on which the star-product is well defined. This space of functions becomes a Fréchet algebra as well as a pre-C * -algebra. Basic properties of the star-product are proved and the extension of the star-product to a Hilbert algebra and an algebra of distributions is given. A C * -algebra of observables and a space of states are constructed. Moreover, an operator representation in position space is presented. Finally, examples of weakly exponential Lie groups are given.

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Section: Star-product On F (M)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deformation quantization on the cotangent bundle of a Lie group

Domański¹

2018

Preprint

View full text Add to dashboard Cite

show abstract

Deformation quantization on the cotangent bundle of a Lie group

Domański

2021

Journal of Mathematical Physics

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We develop a complete theory of non-formal deformation quantization on the cotangent bundle of a weakly exponential Lie group. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on which the star-product is well defined. This space of functions becomes a Fréchet algebra as well as a pre-C*-algebra. Basic properties of the star-product are proved, and the extension of the star-product to a Hilbert algebra and an algebra of distributions is given. A C*-algebra of observables and a space of states are constructed. Moreover, an operator representation in position space is presented. Finally, examples of weakly exponential Lie groups are given.

show abstract

Homogeneous star products and closed integral formulas

Cited by 2 publications

References 17 publications

Deformation quantization on the cotangent bundle of a Lie group

Deformation quantization on the cotangent bundle of a Lie group

Deformation quantization on the cotangent bundle of a Lie group

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