کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8255480 1533709 2018 41 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Quantum Koszul formula on quantum spacetime
ترجمه فارسی عنوان
فرمول کوانتوم کوشول در فضا زمان کوانتومی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
چکیده انگلیسی
Noncommutative or quantum Riemannian geometry has been proposed as an effective theory for aspects of quantum gravity. Here the metric is an invertible bimodule map Ω1⊗AΩ1→A where A is a possibly noncommutative or 'quantum' spacetime coordinate algebra and (Ω1,d) is a specified bimodule of 1-forms or 'differential calculus' over it. In this paper we explore the proposal of a 'quantum Koszul formula' in Majid [12] with initial data a degree −2 bilinear map ⊥ on the full exterior algebra Ω obeying the 4-term relations (−1)|η|(ωη)⊥ζ+(ω⊥η)ζ=ω⊥(ηζ)+(−1)|ω|+|η|ω(η⊥ζ),∀ω,η,ζ∈Ωand a compatible degree −1 'codifferential' map δ. These provide a quantum metric, interior product and a canonical bimodule connection ∇ on all degrees. The theory is also more general than classically in that we do not assume symmetry of the metric nor that δ is obtained from the metric. We solve and interpret the (δ,⊥) data on the bicrossproduct model quantum spacetime [r,t]=λr for its two standard choices of Ω. For the α-family calculus the construction includes the quantum Levi-Civita connection for a general quantum symmetric metric, while for the more standard β=1 calculus we find the quantum Levi-Civita connection for a quantum 'metric' that in the classical limit is antisymmetric. This suggests to consider quantum Riemannian and symplectic geometry on a more equal footing than is currently the case.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 129, July 2018, Pages 41-69
نویسندگان
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