Wick Rotations in Deformation Quantization

Schmitt, Philipp; Schötz, Matthias

doi:10.48550/arxiv.1911.12118

Cited by 2 publications

(2 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus this approach can be seen as complementing the previous strict deformation quantizations by new and different examples. A detailed overview on these ideas can be found in the review [56], the original results are in [2,16,17,32,47,48,51,55].…”

Section: Introductionmentioning

confidence: 99%

Convergent star products on cotangent bundles of Lie groups

2022

View full text Add to dashboard Cite

For a connected real Lie group G we consider the canonical standard-ordered star product arising from the canonical global symbol calculus based on the half-commutator connection of G. This star product trivially converges on polynomial functions on $$T^*G$$ T ∗ G thanks to its homogeneity. We define a nuclear Fréchet algebra of certain analytic functions on $$T^*G$$ T ∗ G , for which the standard-ordered star product is shown to be a well-defined continuous multiplication, depending holomorphically on the deformation parameter $$\hbar $$ ħ . This nuclear Fréchet algebra is realized as the completed (projective) tensor product of a nuclear Fréchet algebra of entire functions on G with an appropriate nuclear Fréchet algebra of functions on $${\mathfrak {g}}^*$$ g ∗ . The passage to the Weyl-ordered star product, i.e. the Gutt star product on $$T^*G$$ T ∗ G , is shown to preserve this function space, yielding the continuity of the Gutt star product with holomorphic dependence on $$\hbar $$ ħ .

show abstract

Section: Introductionmentioning

confidence: 99%

Convergent star products on cotangent bundles of Lie groups

2022

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Convergent Star Products on Cotangent Bundles of Lie Groups

Heins¹,

Roth²,

Waldmann³

2021

Preprint

View full text Add to dashboard Cite

For a connected real Lie group G we consider the canonical standard-ordered star product arising from the canonical global symbol calculus based on the half-commutator connection of G. This star product trivially converges on polynomial functions on T * G thanks to its homogeneity. We define a nuclear Fréchet algebra of certain analytic functions on T * G, for which the standard-ordered star product is shown to be a well-defined continuous multiplication, depending holomorphically on the deformation parameter . This nuclear Fréchet algebra is realized as the completed (projective) tensor product of a nuclear Fréchet algebra of entire functions on G with an appropriate nuclear Fréchet algebra of functions on g * . The passage to the Weyl-ordered star product, i.e. the Gutt star product on T * G, is shown to be preserve this function space, yielding the continuity of the Gutt star product with holomorphic dependence on .

show abstract

Wick Rotations in Deformation Quantization

Cited by 2 publications

References 22 publications

Convergent star products on cotangent bundles of Lie groups

Convergent star products on cotangent bundles of Lie groups

Convergent Star Products on Cotangent Bundles of Lie Groups

Contact Info

Product

Resources

About